How does competition influece adaptation?

You either win, or die. If you win, you get to spread your successful genes to the next generation, and they'll either win the same, win better, or die. The win-betters will often times have better breeding opportunities than the regular winners, and the regular winners obviously do better than the dead ones.

Biological competition takes many shapes, from being able to get food more efficiently, to doing the best mating dances, to being able to out fight someone else, to being better able to cope with changing environmental influences, to being able to digest and get more nutrience from a new food sources, and so on.

The better you are at overcoming obstacles, the more chances to breed, the more chances successful characteristics can slowly change to become more successful.