Bound items are a feature implemented in MMORPGs to avoid abuse of twinking.
Bound items are designed to prevent them from being shared with other characters, to avoid easily making overpowered lower level characters. If you have a bound item, it can (generally) be sold to in-game vendors, but it cannot be traded to another player.
Unbound items, however, can be freely traded from player to player, and can be used by players who aren't the ones who initially obtained the item (whether from quest, random drop, or by purchasing it from a vendor), assuming that the player meets all of the other requirements for the item.
Bound and unbound is not random. Quest items are typically bound, as they are the reward for that character completing the quest, and therefore it is expected that that character will be the one to use it. The same applies for specific reward drops from difficult encounters, such as raid or group instances.