The diamonds originally belonged to Ray Bulgarin, the man Niko used to work for back in Bosnia. They were stolen by a club owner in Liberty City named Gay Tony. Ray Boccino worked out a deal with the Lost biker gang (his wife is friends with the Lost), in which the Lost would steal the diamonds from Tony, hide them trash bags, and then Ray would collect them (Ray worked it out this way so if anything bad happened, the Lost would get all the heat for stealing the diamonds). Ray's guards try to rip him off and keep the diamonds for themselves, but Ray has Niko kill them and return the jewels.
Ray sends Niko to meet with Johnny, leader of the Lost, to sell the diamonds to a dealer named Isaac. The deal is ambushed, so Johnny runs off with the money, the diamonds find their way back to Tony, and Isaac runs off empty-handed. The botched deal causes a rift between Ray and Isaac, so Ray sends you to kill Isaac while sending his own men to deal with Johnny and reclaim the money (we're never shown what comes of this).
Ray and the McRearys work out a new way to get the diamonds (again) from Tony. They kidnapped Gracie Ancelotti, the de facto head of the Ancelotti family, because she's friends with Tony. Niko and Packie arrange to exchange Gracie for the diamonds, which they do, until Bulgarin shows up and ambushes them. Bulgarin leaves his men to reclaim the diamonds and kill Niko, but the guy who picks up the diamonds decides they'd all be better off if they were gone forever, and so throws the diamonds into the back of a garbage truck.
A little later, a homeless man is reported to have found the diamonds at the dump, and he uses them to leave to Vice City and open up a business.
