Invoke is an illusion spell available to the fighting units of Genny, Silque and Tatiana, and it's one of the strongest tools in all of the game, right up there with Mila's Turnwheel. Each of the three can summon a different type of illusion, each of which are equally to the next. Genny can summon extra soldiers to help in the battle, Silque can summon Dread Fighters to assist the cause, and Tatiana can summon Pegasus Riders to attack foes as well.
Genny's soldiers are weak, but she invokes very early and the opposing enemies love to focus in on her soldiers before your own. Silque's Dread Fighters are the quickest and strongest illusions fighters by far, but she can't acquire them until very late in battle. Tatiana's Pegasus Riders are the weakest of the bunch and are usually too frail to do any real damage; Tatiana is more useful with her healing spells instead.
But be aware that you will be losing out on some experience when you use Invoke, as illusions will not gain experience for their character when they participate in battle.