Fuga: Melodies of Steel 2

Affinity level is basically the bond between 2 characters. as they raise, they will unlock skill attacks. Max level is 10. once you are at 10 you should break the group to level other characters.

To raise the level, you either

Group them together in battle.
Talk to them in the intermission
Do Laundry with them in intermission.

There may be other ways as well, but the 3 above are the primary methods to increase Affinity.

I would not focus too much on this as it will come naturally towards the later part of the game.