These are simplified, so I hope people will bear with me:-
V.1 = speed beyond which it is not possible given the length, slope and condition of runway available, temperature, pressure altitude and weight of aircraft to stop without running off the end. It actually has two definitions, and I won't go into the other, which is more performance- and structure-related, but this is the worst-case scenario. Beyond this speed, even with an engine failure, you are going to take it into the air and then sort it out.
V.R = Rotate speed. Obvious, really. Dictated by the manufacturers, based mainly upon weight, temperature, pressure altitude and flap settings. V.R always>=V.1.
V.2 = Speed to be held crossing a 35 foot screen at the end of the runway. Generally considered to be take-off safety speed. Basically, with gear down and take-off flap, you can stay in the air at this speed and still have an engine failure.
Lots of other speeds called different things by different manufacturers and different operators, but these are the most important ones.
Hope that answers your question.