Telepathy is a form of communication where the user is able to transmit information vast distances, sometimes even across hundreds of light years, just by using his/her mind. The user would focus his/her/its mind for however long as they slowly channel information to whomever they wish. This is especially useful when it comes to warfare as users can transmit battle tactics or any form of information which the reciever may find helpful.
There are many advantages to Telepathy. Obviously the first advantage is that it is untraceable by all lifeforms, except the ones that have also mastered the art of telepathy. Another advantage of telepathy is that there is no limit to how far you can send the information and that the other person does not have to have mastred the art to gain information. A major disadvantage however is that it takes countless decades to master this art and even then it is not certain that it will stay with you.
Telepathy is used mostly by the Protoss, as they evolved without mouths and so it is their primary form of communication. They can use telepathy to communicate with all races in any language, however the reciever cannot communicate back telepathically. As they tend to engage in telepathy as a form of communcation (within range of the other person), this is not usually a problem as their sense of hearing is fine and the other person can simply talk back.