KERS stands for Kinetic Energy Recovery System. It's a system similar to those used in many hybrid cars: It recovers the kinetic energy of the vehicle when braking and stores it either mechanically in a flywheel or electrical in a battery or capacitor. This energy is then used later under acceleration. The use of KERS in Formula is limited to an additional 60kW (82PS) for 6.6 seconds per lap controlled by the driver. In 2014 they plan to double the allowed power and increase the usage time to 8.3 seconds. The time gained by this system is about 0.3 to 0.4 seconds per lap.
DRS stands for Drag Reduction System and is a adjustable flap on the rear wing of the car. It can be adjusted to reduce aerodynamic drag thus increasing the maximum velocity of the car (10-12kph). It was implemented to promote overtaking and is by FIA activated only if the car is maximum one second behind the leading car (can be altered race by race) and within a defined DRS zone of which there can be two per race. When activated the driver gets a signal on his dashboard and can then use it. The system is deactivated when the driver brakes or released the DRS button after usage. Activating the system reduced downforce thus reducing cornering speed so it can only be (sensibly) used on straights.
Source: Wikipedia