Ok, so I've read the f/stop chart page in New To Photography learning plan

I get that these are the magic numbers that equate to halving the diameter of each aperture (hole) as we go from 1.4 to (1.4)^2 = 2 to (1.4)^3 =2.8
and that if I don't touch my ISO and I want to maintain the same amount of light entering my image I will need to double the speed of my shutter
OR if I don't touch my shutter speed and I want to mainain the same amount of light entering my image I will need to double the sensitivity to light (my ISO)

I understand the relationship between the f/stop being a divisor of the focal length of the lens with the diameter of the aperture

What I don't understand is why I care?

Example:
in the chart -
what does knowing that I will let in the same amount of light if I leave my ISO as static
and I make aperture diameter half the size
as well as speeding up the shutter speed by doubling it
as I would if I left it alone mean to my photo?

I'm (so far) quite comfortable with the math's but I don't understand how understanding that relates to the actual photo?

If it's on the next page, I may regret this post, but I am going to post it anyway.