The Mirror of Mists, called also Illusion and known as the Mask of Mirrors in Age of Legends, has several functions, each performed by a variation of the weave. The effect of this weave is the ability to alter one's appearance.
It has been reported that according to an interview, this weave can also be used to alter one's voice.
Asmodean teaches this to Rand al'Thor which the Aes Sedai embassy from the White Tower try to use when confronting him.  And it is possible that he turned Egwene al'Vere invisible by using this weave or a similar one.
Mesaana often uses this weave to mask her voice and to make her look like she is made of silver.
As part of Amyrlin Seat Egwene al'Vere's efforts to smoke out Mesaana, Seaine Herimon and Doesine Alwain worked out that the Mirror of Mists can be used to affect what a person is saying into making the listener hear something else entirely.