Fraternization is the act of being friendly with someone you have been told not to be friendly with. You hear it most in the army and in other strict groups: soldiers may be ordered not to mix with the enemy, with local people, or sometimes with other ranks. The word is fairly formal. It does not only mean “being nice”; it carries the idea that the friendliness breaks a rule. In ordinary life people sometimes stretch it for any mixing that a boss or a school would not like. It is not the same thing as joining a fraternity, the US college club, even though the words look close.