Nikon call them Picture Controls, other manufacturers have their own terminology .. but they're all the same thing.
Internal processing of the image in your camera.
The notion of 'straight out of camera'(SOOC), or 'unprocessed' is a strange, and sometimes maligned concept.
Some folks swear by it, other's swear it's a load of rubbish.
The way I see it, unprocessed or SOOC is a reference to the image not being 'shopped' ..or processed beyond what the image originally looked like.
Think blended skies, HDR(although that one is being blurred now as many cameras do HDR) cloned in or out elements .. even focus stacking is now possible in camera(I think Olympus's do it)

So first off lets not get bogged down in the arguable concept that is SOOC, or unprocessed.

What Picture Controls do in a Nikon camera is process the image to a specific taste.
All images have some form of picture style edited into the image.
The way I understand it, even when you open a raw file in a thirdparty raw converter, even tho the thirdparty converter doesn't necessarily respect the manufacturer's picture style(basically a tone curve + colour enhancement + any other enhancements), those thirdparty raw converters add their own processing into the raw file to give it a look.
A raw file viewer program called Rawdigger is supposed to allow you access to an unedited unprocessed raw file.
I tried the evaluation version, didn't understand it, couldn't see any reason to continue with it .. and it's supposed to be for hardcore ETTR, best possible data capture and the more scientifically inclined type of photographers.

So you want a specific look to your images SOOC from your Nikon camera, then you want to play with Picture Controls.
To do this you need one(or more) of Nikon's own three software. One of which is current(and hence supported) and the other two are not.
They are CaptureNX-D(current), and the older CaptureNX2 and ViewNX2(both no longer supported .. but still work with older cameras)

There is a bit of a caveat to watch for here too for some cameras/models.
There are two types of Picture Controls, which in most situations the user needn't worry about. This only comes into plat, if you want the picture control for use in the camera!
The two types of Picture Controls are an NP2 type(the most recent camera models(eg. D750, D810, D7200, D610 .. etc) You need to check .. I can't remember is a D610 is new or old.
The older type of Picture Controls(from here on will be called <PC>) are an NCP type.
This will be obvious in the software. Just be mindful of it.

While I'm going to use ViewNX2 for the Picture Control editor tips, you can easily use CaptureNX-D which will provide the same Picture Control editor software(as a popup window)
You need to have either or both of those two software depending on your camera(s).
Capture NX2 does have a Picture Control editor too, but it's the older v1 software and it doesn't have any understanding of the newer NP2 file types(only the NCP types).

So to invoke the Picture Control editor, you open your Nikon software and look for the Launch Utility iconnot very intuitive, but that's Nikon for 'ya!)
** Note in CNX-D, you access this software via the Tools->Launch Picture Control Utility2 method **
#1_Picture Control-Launch Utility.png
Look for the button in the Adjustments tab. (alternatively it's in File->Launch Picture Control Utility2).

Hit the button and you see this:
#2_Picture Control-Initial settings.png
Two things are assumed here. you have a raw file selected and active in the Nikon software. You can't get to the editor if you have a tiff or jpg file selected and active!

1: look for the file type for the relevant <PC> you need for your camera. Although you can use a newer (NP2 type) <PC> on an older camera type raw file, you can't save the newer type to the camera.
So if you want the Flat look <PC> in your older D800, D600, etc camera .. bad luck. It doesn't work. But you can edit an older <PC> to look like the Flat <PC> Nikon made.

Also, It's very important you start with a particular looking <PC> as a basis for your edited <PC>. If you start with the Landscape look(contrasty/sharp/hard/saturated), it's going to be harder to make it look unsaturated/flat/colourless/etc.
The new <PC> you create is based on the one you chose just below the file type selection box.

2: By default, when you first open the Utility it starts at this stage, where you can't really do much. You need to activate the editing tools. Hit Manual Adjust and then it should also have another dot marked, just under the Use Custom Curve option. It's a bit backwardly designed, but that's Nikon for 'ya!

3. If you hit the custom curve icon, you then activate the custom curve tool. This is where the power of the Utility lies.

#3_Picture Control_edit - save - export.png

1. I've edited the tone curve here. originally it will look like an average linear tone curve, shadows start at 0,0, and a straight line up to highlights at 255, 255.
As you can see, I've inverted the tone curve. The white stones on the image on display now look dark grey/black.
You can add an S-curve, or you can edit to your pleasure. But there is a caveat here too. While you can do many intricate things here this adjustment only affects the luminance channel.
That is, as I tried to invert(ie. turn a positive image negative .. which you traditionally do the other way.. invert a neg into a positive image).
So no colour reversal is possible with this method(which bummed me out as it's what I wanted it all for!)
Even considering this, it's still fairly powerful and a lot more finely tuned than the simple 3 step slider system.

(actually that's one of the key differences between NCP and NP2 <PC> file types. Plus the added clarity sliders and whatnot!)

2. Saving. Note how I have Standard highlighted up near the 1 arrow. That is, Std <PC> has been used here. Once you've experimented a bit with the look you're after, you need to hit the save button down here. If you don't, and close the program, it will ask if you want too anyhow. To load onto the camera, you need to save the edited <PC>

When you hit save, it will ask for a name. In the next screencap I named mine(for this purpose Standard-Wild test) The Standard part of the name comes from the used base <PC> I selected.
Obviously if you start with Landscape, it will offer Landscape - ??. give it an obvious name(it will make a difference later on the camera)

3. Once saved, where it says Import in my screencap, the other three buttons will become highlighted too.
You want to look for the Export box. BUT!!!!!

But before you so hit the export box, you need to have a camera formatted card in the card reader(or maybe camera .. or whatever you do!). But without a properly formatted card connected to the computer, the Export dialogue will fail(see below)

#4_Picture Control_saved - named - export(fail).png

1. note the file name
2. hit the Export button
3. If no media is present, or the media is incorrectly formatted, this warning opens up.

Very annoyingly, if you did everything right, nothing alters you to the fine fact! Typical Nikon! .. you do good, they don't recognise the point
Anyhow, if you did everything right had a properly formatted card, the right <PC> type chosen and all the stars aligned, to confirm that the export went well, navigate to your media card, look for the Nikon folder/directory, look in there for the CUSTOM PC folder, and iin here you will find where your <PC> was saved too. Don't touch this file(you can't do anything with it anyhow).

#5_Picture Control_ choose slot - export - then nothing.png

Here we find that I finally exported my wildly edited <PC> to slot 1 in the <PC> list available. I think it goes down to as much as 99.. so you can load basically an infinite number of <PC>'s.
When you go into the CUSTOM PC folder on your media card to find the <PC> you just made, it will be called PICCON0x.NCP, where x represents the slot number you chose to place this <PC>
So had I chosen slot 99, PICCON99.NCP will be created on the media card.

From here it's easy peasy to get the <PC> into your camera and loaded up.
This part assumes a Nikon camera with the ability to use Picture Controls.
Place the card back into the camera, with this PICCON file definitely created and saved as per the Utilities doing.
In your camera, you need to find the <PC> feature menu. It's usually located in the Menu - Shooting Menu - Manage Picture Control section(or something like that).
Select this menu item, and in here, you use the Load/Save option .. obviously the load part in the next menu item in here!
On my cameras it called Copy to camera. The PICCON file is placed into the correct location on the card for the camera to find it.
Once you activate the copy to camera menu item, it then shows you a list of the actual names you used to save the <PC> in the Utility .. not the PICCON file you saw in the CUSTOM PC folder on the card. The only limitation is the length of the file. I see Standard - Wild te(missing the st in test!), so make your <PC> names make sense(to you).
During the load to camera stage, it should offer you an option for which camera slot to place the <PC> file, and then maybe if you'd like to rename it again.

Once the camera has uploaded the <PC> from camera to card, you then need to do one more step to get it active.
Just as with any <PC> in camera in use .. it has to be loaded via the Set Picture Control menu in Shooting Menu.
Once your camera has uploaded the <PC> from the card to the camera, you can safely delete the PICCON file from the card(it's no longer needed).

So once you have the <PC> about to be loaded as the current <PC> to be used, the camera should offer some options to tweak it.
If you've used the Custom Curve tool, you'll notice that Brightness and Contrast are greyed out .. and you can only alter sharpness, saturation and hue in the tweaking section.
The Brightness and Contrast values say USER in greyed out text.

When you select a new <PC> in camera be sure to press the OK button to load it properly. Pressing the right arrow on the multi way keypad doesn't work .. you NEED to press the OK button to confirm.
Obviously if you make a wild edit as in my test, and you shoot jpg, then the file is set this way and there's nothing you can do about that.
But if you shoot raw(NEF) mode.. you can easily undo it and use a different <PC> via Nikon's software.

Lastly: note that these <PC>'s can be shared amongst other Nikon users(as long as they are compatible with your camera!)
So if you feel up to creating something that you reckon others may find useful, then save the PICCON.NCP(or NP2) file and send that to the interested other party.

Note over the years there have been some sites dedicated to sharing Picture Controls around.

I'll add to this post with some of the sites/info I've found over the years.

Hope this helps .. even tho it was long and tedious!