A data ghost was the name given to a digital impression of a living consciousness that sometimes remained in the Neural relay of 51st century comm. systems after its occupant had died or been killed. It is considered a very disturbing and uncomfortable thing to watch and listen to a Data ghost; Donna Noble even called it the most horrible thing she had ever experienced.
The dead person would thus appear to be able to still be alive, and be able to communicate, though they quickly became 'confused' due to the degradation of the stored data pattern and start to repeat themselves, or make illogical statements, until eventually the pattern failed. The Doctor described the effect as a footprint on the beach with the tide coming in. The pattern would continue to fade until someone manually disconnected the unit.
The Data Ghost would communicate through the speaker on the suits, much to the horror of the witnesses to their death. Three of River Song's exploration crew experienced the data ghost phenomenon upon their deaths in The Library: Miss Evangelista, Proper Dave, and Other Dave.
However a Data Ghost can be uploaded onto a hard drive and thus would result in the person 'cheating death' while living inside a computer, the Doctor did this as to save River Song, who died but whose consciousness was briefly retained within a specially designed neural relay the Doctor had installed within a sonic screwdriver he had given her at some point in his future/her past. (DW: Silence in the Library/ Forest of the Dead)
The Gråttites used similar technology to have their last thoughts hung alongside their portraits in the Whispering Gallery on Grått. (IDW: The Whispering Gallery)