'Head games' is a special term specifically used in the context of romantic relationships. It refers to when one partner in a relationship uses a sort of psychological warfare on the other, being covertly dishonest and manipulative in an attempt to get some specific response from their partner. When someone mentions that they want 'no head games', they mean they're looking for a partner who'll be honest and upfront with them and won't try to manipulate their subconsciousness behind their back.