A mechanic is a way in which your game character moves or is controlled. Most of the time the game's normal mechanic is in effect, but there are debuffs that can change your mechanic. Debuffs that impose mechanic-altering effects come in all dispel types, and some have no dispel type at all, meaning that they either must run their course and expire over time or have a specific way in which they can be removed.
You can't control your character, who stands still, usually with hearts floating above his/her head. Some classes' PvP trinkets cancel this effect, as does the Undead racial ability Will of the Forsaken.
You can't control your character, who wanders aimlessly. There may be items that help remove this effect, and these would of course be usable in this situation.
The damage dealt by every melee attack you make is reduced.
You move slowly. This is a lot like the Snare mechanic, although it has the added effect of knocking you off your mount, if you're on one to begin with.
You run uncontrollably away, out to a certain radius, then mill about randomly, also uncontrollably. PvP trinkets for many classes remove this effect, as does Will of the Forsaken.
(Examples: Mind Control)
You are under the control of another player.
(Examples: Polymorph (duh!))
This is basically a combination of a Confuse effect and a Transform effect. The reason why it's a separate mechanic from those other two is that there are items (for example, the PvP trinkets) and class abilities (such as the Druid ability to shapeshift) that remove both components of a Polymorph effect.
You are frozen in place, attached to the ground.
You are unable to cast spells.
You move more slowly than normal.
You are unable to move, cast spells, or use items, with the exception of those which allow you to break free of stun effects, of course.
You look like something else. This is usually combined with a Confuse mechanic, but nothing says that it has to be.