A revenant is the ghost of a person which returns to a particular place after death. This place is usually tied in with either the life or death of the person.
If the person in question came to an unnatural end, i.e murder or accidental death, then the events of the persons end can condemn their spirit to re-enact the scene over and over until they either come to terms with it and forgive the perpetrator or they are exorcised.
The other side to a revenant is when the person in question had strong ties or feelings for the place they choose to remain in. Classic examples are their house or a loved one's residence.
In the second case, the revenant is usually harmless although it usually will still alarm people where as in the first case the revenant may also act like a poltergeist as they are not at peace.