The Charm spell makes the victim think (for a short time) that the caster is their closest friend, or even beloved one, and unable to resist them in any way or just part with them. Eirena once accidentally cast this spell on Lysa, causing the latter to follow her fanatically for a forthnight. When Lyndon attempted to flirt with Eirena by asking her how did she become so good at 'charming' others, she took his words literally, saying that she practiced this spell times beyond count.
Charm is a magical effect in Diablo III, mostly used by Eirena (as well as Lysa). The other notable Charming effects are those of The Tormentor staff, Henri's Perquisition mojo and Overwhelming Desire amulet. As of patch 2.6.0, Necromancers can use it as well, via skill runes of skills like Bone Spirit.
For gameplay purposes, Charm makes the affected enemy briefly fight on the caster's side, attacking their foes and unable to perform any offensive actions against the caster (and their allies). If Charmed while there are no other enemies around, the victim will just stand idle or follow the caster. While charmed, the other enemies will see the victim as a hostile target, and the caster's allies may still attack that target at will. Target's special abilities and skills may still be used, and will benefit the caster, or at least bring them no harm. This way, Charm is a more potent effect than Confusion.
CC resistance reduces the duration of Charm. Bosses are immune to it.
Unlike Confusion, Charm could initially affect players as well as monsters. In the released game, it can no longer affect players, even if they somehow manage to put such an effect on another player in PvP.