I always see this being displayed over the character's profile during battle and when I select a target. So what do the numbers mean exactly and how are they calculated?

It lists the percentage a character has to combo with another character. (when all the character surrounding the attacking character join in with the attack) There are a wide amount of factors that go into combos such as weapon, class, pupils, even the chapter of the game!(In regards to Adell and Roz)

For example, same weapons types, combos including tutors and pupils, Gloves ,and Beast Masters comboing with monster all get a bonus to pull of a combo.

I think you might be referring to the combo damage bonus, which goes up each time you attack without moving.

Yea, it was definitely not the team attack percentage. It was the other one that had something like "COMBO ADJUST XX + XX%" or something to that effect. Does anybody know what the numbers mean exactly?

Yes, your character does essentially that much extra damage (e.g., +10%) when attacking, and he/she also has an increased chance to hit the target. The counter is increased every time your character attacks, counterattacks, or uses a special move, and it is reset every time your characters moves using the "move" option (being thrown doesn't reset it). I believe also doing something like switching to special attacks after normal attacks resets it, or something along those lines (maybe it works in reverse).

I can see how great that would be for battle strategy, particularly when you're up against ninja or other high-speed/evade types, or if you're using axes. =D