Telepathy is regarded as the paranormal acquisition of information from the thoughts, feelings or activity of another person without using the five senses. In other words, it's the ability to read someone's mind. Matt Parkman can hear people's thoughts. He cannot as yet receive images, memories or emotions from others as his ability appears limited to only hearing a person's current thoughts as they're thinking them. He must also be within a certain physical range, but he doesn't need to see them - he can 'phase-hear' through solid objects.
Matt has limited control over this ability, as does Peter. When the two met they both experienced a kind of intense 'static' that caused both to wince in pain. Matt uses his ability best when he can actively focus on the thoughts of a particular person, as his ability to 'filter out' unwanted thoughts is not refined.
It is interesting to note that many magicians and psychologists have demonstrated techniques and results similar to those of popular psychics, but offer psychological explanations. They have developed complex techniques of questioning people and reading their body language and voice tone responses.
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You culd find out what your partner really wants for Christmas, or what your parents think about your partner, friends and so on.
And you gotta love the Peter/Matt feedback loop. Peter thinks something, so Matt hears it, so Peter hears it, so Matt hears it...
As for the moment when Peter and Matt meet and "burn each other" - I imagine with Peters power, it would have been like a feedback loop between them as Peter seems to have a little "trouble" controlling the power he receives. Matt "looks into" Peter and at the same time
uno, under 'telepathy'.