Fame points is what you gain by defeating a human opponent. Fame points awarded if you beat someone during attack (Battle button on lower left-> Find an opponent) or if you were able to defend your camp so that attacker didn't gain 50% damage (didn't gain any stars). Algorithm to calculate is complex but it boils down to how much stronger/weaker you than your opponent. Battle with weak opponents yield small amount of fame (even 0 in some cases!), battle with strong opponent yield a lot of fame.