The bottom floor of an F1 is shaped like an airfoil at the rear end, air that flows underneath it creates downforce.
With a 'blown diffusor' the exhaust gasses pass through this diffusor too. Normally when you release the throttle the amount of gasses is very low, but this season some F1 cars found a way to program the engine control unit so that it still injects fuel when the trottle is released, but by cutting the ignition the fuel ignites in the hot exhaust pipes, creating a steady flow of hot gasses even when the throttle is not used thus creating downforce.
This system was used in rally cars several years ago btw, to keep the turbo spooled up all the time preventing turbo lag.
F1 cars have a switch on the steering wheel to select 'engine mapping', basically let them choose between several programs for the engine control unit. Variables they can choose include more or less rpm's, fuel consumption, rain settings (slower throttle respons) or more downforce created by the exhaust gasses. Obviously that uses more fuel which is why it's used more in qualifying.