Neural relays were devices used in the 51st century to let people send "thought-mail" by point-and-think technology.
In the 51st century, when someone died, their consciousness might leave an imprint in the neural relay. Using its communications device, the data ghost could, for a short time, talk to other people before deteriorating, starting to repeat itself. While this phenomenon usually lasted only a few minutes, Anita mentioned that her grandfather had "ghosted" for an entire day and kept talking about his shoe-laces.
Miss Evangelista's data ghost wanted to talk to Donna, but deteriorated to repetition of "ice cream". Proper Dave's data ghost kept repeating, "Hey, who turned out the lights?" (TV: Silence in the Library) Other Dave kept saying, "We should go, Doctor!"