I read a book about the matter. Looks like when a trainer encounters a wild Pokemon, the trainer's Pokemon and the wild Pokemon fight to see who is stronger. If the wild Pokemon is defeated, you can try capturing them, and your superior strength inspires them to join you instead of breaking out of the Pokeball.

[He got all that from a children's book. They seemed the best to explain such concepts in simple ways, yet he's not sure he fully understood it. Culture shock, you know!]

I'm not sure how appropriate it is, but that seems to be how it worked. I doubt there will be any fights with wild Pokemon anytime, though.