Finesse is essentially a reward for effective use of combat skills. Savvy use of one's skills results in higher gains of Ultimate points. Once significant points are earned, an ability slot in the combat UI will flash indicating a special Finesse attack can be activated. These special attacks are called Ultimate Skills.
Ultimate Skills each cost a specific amount of Ultimate to activate; they do not consume Magicka or Stamina. These skills level up the more they are used, as with most skills. Additional Ultimate can be gained through good use of skills and through certain passive skills that increase Ultimate gained.