Rebbetzin is the title of the wife of a Rabbi, though we tend to think of it more as a shul rebbetzin. If she prefers, she can simply be called “Mrs (whatever).” Most Rebbetzins are referred to as such when their husband is the rov of a shul or Rosh Yeshivah type. It confers NO special talents or bina yesaira upon her (she could even technically be a total am haaretz, but that is not so likely that a rov would have such a shidduch nowadays), and she must ALWAYS ask her husband for any shailah presented to her. The title conjures up a certain image, but it really is simply the way one may address the wife of a man who has smicha and is called rabbi.
Many rebbetzins, who are learned women, give shiurim to the ladies in their shuls, but that is not a requirement of the title “Rebbetzin” (it might be expected, however, by the shul Sisterhood, when they hire the rov). Otherwise, a typical Rebebtzin might do little else but make cholent for the shul for kiddush, in a shteeble type situation. Her strengths might lie more in being an ear for the women, to relate back to her husband, when there are issues that need to be conveyed to him in a tzniusdig way. If well-educated or highly-motivated, the rebbetzin might take a more active role in community issues. I have seen rebbetzins on both sides of the spectrum, some very active, and some extremely passive and non-involved. Both were rebbetzins.