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!"
Anita was killed by the Vashta Nerada, but had no obvious data ghost, as the Vashta Nerada had learned to talk through the neural relay.