Why ``adversary'' and ``challenger'' and what are typical roles of those?
Suppose you are a member of a mailing list or of an anonymous cryptographic site. Now suppose there is some "new guy" who just joined and makes bold claims about having broken some cryptosystem. Now of course because you don't know anything about the "new guy" you don't believe them. Naturally they're really insistent, so you agree to challenge their claim that the cryptosystem is broken. This makes you, the skeptical person, the challenger.

Of course because the other is trying to break the cryptosystem they're the adversary against which the cryptosystem tries to hold up. Now of course you, the challenger, know that a total and complete break of any cryptosystem (e.g. ciphertext-only attack) is an unrealistic capture of the reality, so you agree to provide the adversary with some ressources, e.g. answering requests for encryptions.

So in a sense security games are protocols that allow adversaries to convince challengers that they broke a security property in the most reproducible and convincing way (e.g. because the adversary clearly at no point has access to the key).