Telepathy pendants were, aside from their written language, (TV: A Day in the Death) the primary method of communication among Arcateenians. They spoke to one another by simply thinking, which Mary — an Arcateenian criminal — found much preferable to the archaic oral Earth languages, with a "pre-arranged and finite number of words".
To humans, not accustomed to others reading what was in their heads, it was the psychic equivalent of an eavesdropping device, allowing the reader to listen to the thoughts of others. Mary gave Toshiko Sato the pendant as a gift. Passing herself off as a human at the time, Mary pretended that she had obtained the pendant on the alien artefact grey market.
When worn around the neck, the pendant let Toshiko eavesdrop on the thoughts of people around her. This worked poorly because of the overwhelming number and volume of thoughts that Toshiko exposed herself to in this way, as well as confusing her as to whether her thoughts originated in her own mind or those of other humans. Mary shielded her thoughts. When in Jack Harkness's proximity, she could not read his at all. Jack could project thoughts to her, if he chose, but she could not read his personal thoughts, possibly because he was "dead".
It allowed a person to hear both conscious thought and subconscious thoughts of an individual. Toshiko heard Gwen Cooper's and Owen Harper's conscious thoughts about their secret affair. When she read Ianto Jones' mind, she not only picked up his pain over Lisa Hallett's death but also the darker side to his personality.
Talking it over with Jack and unsure what to do, Toshiko decided that the pendant's abilities were powerful enough to change the world. After talking matters over with Jack, she made her decision: she crushed it underfoot, destroying it forever. (TV: Greeks Bearing Gifts)