Tradition definition: "a series of persons relieving one another or taking turns." The term 'relay' can be applied to shift work.
In some message-board communities on-line a relay can also be a reference to a game such as a use of the infamous 'Word Association'. It's also used to refer to a fictional story written by multiple writers who take it in turns to add their own chapter; typically concentrating on their own specific character.
A multi-author story written on an online forum, through e-mail, or through the post. The story is written chapter by chapter (give or take) by the individual authors, each adding their own plot additions and twists.
The authors have control over ALL the characters as well as the power to direct the flow of the plot.
"Did you see what DW wrote for the relay?"
"Yeah. I can't believe he killed off the emporor."