Drafting is a key element in bicycle racing.
In a properly prepared road bicycle, the majority of the energy required to go forward after about 12 mph is used in overcoming wind resistance. So naturally, reducing wind resistance eventually becomes easier than turning the pedals harder. This has led to aerodynamic equipment and riding positions, but when it comes to races, drafting is the key.
The winning strategy in most races involve being in 2-5 spot, behind someone until near the finish, where you can sprint faster than the guy ahead of you that was fighting more wind resistance for the past few minutes. If the guy is sufficiently strong, however, he is still faster than you even after going against wind resistance, and you lose.
People without good finish sprints try to go off on their own, before the finish. At least this way, they are not giving anyone a good draft in the lead up to the finish.
Because wind resistance is dependent on the speed, anything that would reduce your speed makes drafting less important. Therefore, wind resistance is not quite as important when going up steep hills.
Interestingly, in Iron Man-style triathlons, drafting is not allowed.