Possession is the state of a canon character possessed by a Sue-wraith. It is a common feature of bad slash, but can be found in non-slash missions as well. It should not be confused with regular OOCness or character replacement.
The signs of possession are abrupt, unexplained changes in appearance, behavior, or both. Changes can range from the minor but baffling, such as replacing their wardrobe and turning from a reasonable, intelligent person into a whiny brat, to the serious and potentially offensive, such as falling in love with a mortal enemy or abusing a beloved child. However, they are always Sueish in nature, increasing the character's "specialness" and replacing meaningful conflict with token obstacles that are easily brushed aside when they are no longer needed.
Ho!mione is an apt example of this type of Sue. She is a common character replacement of Hermione Granger who gets a makeover, changes her clothes so that they're very revealing, and romances Draco Malfoy. The canonical Hermione Granger (not to mention the canonical Mudblood-hating Draco) would never wish to do such things, but her Suethors do, to the detriment of her character and to canon.
Possessed characters can also be identified by the Suefluence they exert on the people around them. In most cases, they force others to accept their altered state without question—thus, Harry admires Ho!mione's new look and is just thrilled that she's snogging Draco. In other cases, they may force others to react with uncharacteristic negativity only to be derided for being intolerant or just plain evil, thus showing how perfect and good the possessed character is by comparison. Ron is commonly targeted for this kind of straw-man treatment in Harry Potter Suefics, regardless of who stars in them.
The solution for possessed canons or agents is almost always an exorcism. After exorcisms, displaced Sue-wraiths have been known to possess agents, so appropriate containment measures should always be used.
Victims of particularly strong or offensive wraiths may require a trip to FicPsych for additional help. If they've been forced to do things they would normally abhor, they may need therapy. If they've been pushed too close to 100% OOC, they may need a full personality reboot.