Going to battle with teammates on an athletic field of competition creates a bond that is hard to quantify. The unifying element of the "us against the world" mentality often cultivates lifelong friendships. This brotherhood is nearly impossible to duplicate and the camaraderie shared between teammates can be the one thing that retired players miss the most from their playing days.
The NFL experience is the same, but different. While it is still the same game many of us grew up playing, both competitively and for fun, the stakes are certainly higher when the game is also your profession.