From my operators performance manual:
V1:
"The maximum speed in the takeoff at which the pilot must take the first action (i.e. apply brakes, reduce thrust, deploy speedbrakes, etc) to stop the aeroplane within the accelerate-stop distance. V1 also means the minimum speed in the takeoff, following a failure of the critical engine at VEF, at which the pilot can continue the takeoff and achieve the required height above the takeoff surface within the takeoff distance"
V2:
"Takeoff safety speed. The target speed to be attained at the screen height, assuming an engine failure during the takeoff. This speed must be at least 1.13 times VS in the takeoff configuration"