Check out the topic on GTA Forums:http://gtaforums.com/topic/796634-heist-games-storyline/

About:

San Andreas, somehwere around 80's.
Most powerful and influental people in the country started a revolution in crime by organising elite crime groups whos primary job is to pull heists that were considered impossible. State is going crazy doing everything they can to stop this new threat in the city. One of most famous of the so called Heist crews is funded by Vincet Frey and lead by a former street racer Samwise Adder. Big cash is in question so many other groups are formed aswell making competition to one another. With couple of groups working against each with same goal, government started to call this case: The Heist Games.