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An off spec refers to a role or specialization a player able (or willing) to play while not being specifically geared towards it. This is not to be confused with off tanking or off healing, situations where the player is only intended to intermittently supplement the role of another player already in the group. Rather than re-spec, some players carry multiple sets of gear for these alternate roles. Players who off-spec frequently tend to purchase dual specs; in that case the "off spec" may be the one played less frequently or the one lacking gear as high quality as the usual spec.
Players willing to off spec theoretically have an easier time getting groups, especially if the alternate role and its associated gear is close to the primary one and no one else in the group is able to fill that role at all. However, this can depend on how paranoid a group is about bringing non-minmaxed players to particular instances, especially in the roles of tanks and healers rather than just pewpew. PUGs tend to be less willing than guilds to accept them, so it is good etiquette to mention if you are doing to avoid complaints of under-performance later.
Off spec gearing
This section concerns content exclusive to Warlords of Draenor.
Warlords of Draenor made off sepc gearing much more friendly now that most armor will activate a different primary stat bonus depending on the player spec. Most necklaces, rings, trinkets, shields, and weapons still usually only have one primary stat bonus, so may need kept to optimize the off spec.