A trance medium is someone who goes into a hypnotic state to bring you messages from your deceased loved ones or other guides and ascended masters. This is sometimes called mental mediumship.
In most cases, the medium just conveys the messages that he brings back from others (think Sylvia Browne, John Edward, etc), but a trance medium does more than this. A trance medium enters a light trance and allows the disembodied being to speak straight through them. Sometimes they can sound like the entity they are channeling. Sometimes they even start to look like that being. Trance mediumship usually takes quite a bit of training, and should not be attempted by the inexperienced.