The general concept is completely stopping the target, forcing them to remain in one place, unable to move, but unlike Stun and Freeze, it does not affect the target's ability to attack. Most of the time, Immobilize is used either by ranged attackers to prevent the enemy from coming into close combat, or by melee attackers to prevent enemy from escaping.
In the original Diablo, Immobilize did not exist.
In Diablo II, the only real Immobilize effect is the Necromancer's Bone Prison spell, even though it is simply trapping the target, not actually preventing it from moving. Diablo's Evil Force is not an Immobilize effect: it is only used to block Town Portals.
In Diablo III, Immobilize is fully functional and is a separate effect from Slow. Many skills and items give a chance to Immobilize on hit, and elite monsters may have a Jailer affix that allows them to Immobilize all enemies in range for a few seconds.
Note that turning around does not count as movement and is therefore not prevented by Immobilize. Immobilized target can still attack and use spells normally, provided the target is in range. CC resistance reduces the duration of this effect for both players and monsters. With Ice Climbers, players become completely immune to Immobilize.
Immobilize is a less common effect than Slow, and lasts for a shorter time. It is most dangerous when combined with area of effect damaging skills, as it forces the target to remain in the area.
Any Immobilize effect can be cleared by most skills that allow rapid relocation, such as Teleport. Moreover, skills that force the character to move (such as Strafe, Whirlwind or Tempest Rush), will make the character immune to it while channeled (but will not clear existing Immobilize effects, and cannot be cast while Immobilized).
All Bosses are immune to Immobilize, regardless of its potency.
Immobilize and Slow are not mutually suppressing, and are not interchangeable: that is, for the purpose of whether or not the target is Slowed, Immobilize effects do not count, and vice versa. However, the target may be both slowed and immobilized at the same time.