Hordes are new type of enemy, first seen in Shin Megami Tensei IV. They are a group of demons counted as a single force. A Horde can be made up of a entire group of the same demon or be made up of demons of the same race/mythology. Several Hordes are mini-bosses and bosses in the game.
Despite its display of multiple enemies, Horde is treated as one single entity with more than one turn icon (but much less than the amount of the demons shown). That means single targeted skills will hit the whole Horde once, but using all targeted skills will do multiple hits. The amount of demons of the Horde is merely to notify player the remaining HP of the Horde.