The term All-in is probably derived from poker. It signifies putting all of your remaining chips on the table, thus either cashing in a huge win, or dropping out of the game. In StarCraft terms, this means committing to a single attack which can yield a huge gain, but if it fails you are either 1) very far behind or 2) out of the game. Usually, All-ins are performed by the player who is inferior in Economy.
All-ins can arise from different game situations: They can be planned, for example if a Zerg tries to break a Protoss Wall-in while sacrificing Economy, They can be forced, i.e. a desperate attempt to win the game if a drop has decimated your workers at the mineral line.
All-in can also be used as a verb, as in "to all-in". It means performing an All-in move.