Teyla's ancestors were experimented on by a race called the Wraith. They had Wraith DNA mixed with their own, and through the magic of reproduction, Teyla's DNA still has traces of the Wraith kind. When a Wraith is nearby, she can sense them, and through practice in canon, she's been able to get into their heads and read their minds. The problem is, it's not exactly a secretive practice, and they can get into Teyla's head in return when she does that, and control her.