Well thats a quiet easy one,

The first RepRap was the Darwin printer,
Made by Adrian Bowyer,
His is a British engineer and mathematician, formerly an academic at the University of Bath.

The plan was to make a printer that easly replicated itself, or atleast most parts (plastic parts obviously)
Thats were the REP comes from Replicator, Rap is Rapid (Replicator Rapid)

He made it opensource so everyone could learn about this technology and do there part in it to improve its quality,
That happend and diffrent printer models came, like a few famous ones are Prusa, Rostock/Delta, Ultimaker/Makerbot, CubeUp!

Some made there design Closed source wich is kinda dicky but ye ^^