Spiraling a football takes advantage of a principle in physics called angular momentum. When an object is spinning, it has angular momentum, and without anything to stop it from spinning, will keep spinning in the same direction. When you add a spiral to a football, you give it angular momentum, which makes the football stay in the same orientation with the point facing the direction of the throw while it's travelling through the air. This makes the football throw more predictable and stable because if the ball is not spiralled and it tumbles through the air, it will be pushed around by wind in all directions, which makes the ball harder to catch and it might not land where you think it will land.

With the "nose" of the football pointing in the direction it's thrown, it also may experience less air resistance because the narrowest part of the football is facing into the strongest wind, but this is usually a small effect and the throw accuracy is the main reason footballs are spiralled.