Gear inches is just one of several ways of expressing how far the bike travels for one turn of the cranks. It is useful because it takes into account the diameter of the wheel.
The calculation is (Teeth on chain ring divided by teeth on the sprocket) multiplied by wheel diameter.
The term "gear inches" refers to the equivalent size of a wheel if it was directly driven by the cranks, like on a penny farthing or unicycle, rather than through a chain and gears. A bike with a 72 inch gear travels the same distance per turn of the cranks as a penny farthing with a 72 inch wheel.
If two bikes achieve the exactly same figure for gear inches, they will travel exactly the same distance for one turn of the cranks.
The mathematical variables are the number of teeth on the chain ring, the number of teeth on the sprocket, and the rolling diameter of the wheel. Change one and you will have to change one or both of the others to get the same number of gear inches.
You may find that a larger chain ring and sprocket will be slightly smoother and also result in less wear.
You may find that a larger chain ring and sprocket is slightly heavier and has slightly more aerodynamic drag. I doubt that most of us would notice the effect.
You may find that a smaller chain ring and sprocket gives more ground clearance if you are given to riding on rough terrain.
Of the three variables, the one that makes most difference to the ride is the wheel size. Set up a 700c bike for 72 inches, and a small wheel Moulton for the 72 inches and you will notice a difference, especially riding on an uneven surface.
The gear inches calculation does not take into account the length of the cranks. For modern bicycles, the length of cranks is fairly standard around 165mm to 170mm. Shorter cranks have less torque, but the rider's feet move a smaller distance per revolution. Short cranks mean you can spin faster (in a lower gear) but have to push harder (in a higher gear).
For comparison, unicyclists pay a lot of attention to crank length because unicycles are direct drive and the only variables they can play with are the wheel diameter and the crank length. (Geared hubs are available but are extremely expensive.)