Uppercuts are useful when thrown at close range, because they are considered to cause more damage when at close range. On the other hand, it is likely that a boxer would miss if the uppercut is thrown when the opponents are apart. Uppercuts usually do more damage when landed to the chin, but they can also cause damage when thrown to the body or when landing on the nose or eyes.
As far as the punch's movement, the name says it all: the punch usually initiates from the attacker's belly, making an upward motion that resembles a pirate's hook in shape, before landing on the opponent's face or body. In a conventional boxing combination, it is the second punch thrown, after the jab, but it could either initiate or finish a combination.