I thought I might jump in here just a little even though I don't know a whole lot about the NFL specifically but the rules around the footballs and what not are mostly the same for other sports like Rugby League and Football (some call it Soccer).
I think @Jacoby_Elderfun1 is referring to PSI which is Pounds per Square Inch which is the measurement they use to gauge how inflated a ball is (in this case), the reason they put in strict measurements on something like this is to create an even playing field.
If teams train and play with a, let's say, 8.15psi football and another team trains and plays with an 11.15psi football they would be used to basically two different types of footballs, Imagine these two teams play against each other but the match is played with an 11.15psi football, the team who has been practicing with that type of ball would have an advantage as they would be used to it.
This may seem insignificant but when it comes down to professional play things like these can make big differences and the rules are there to make it as even as possible to make sure the teams are on an even footing when going into a match.
Hopefully, that makes sense!