Takeoff rotation is predicated on the flight data done prior to starting engines. S1 airspeed is calculated, as is V1. S1 is decision, V1 is rotate. V1 can be quite a ways down the runway, especially to somebody observing from the outside. 
That must be the military version, but it is close to the civilian version.
V1 is decision speed. If everything is working right, keep going. If not, stop.
VR is rotation speed. Time to rotate the nose upwards and takeoff.
V2 is engine-out climb speed.
The speeds are based on weight, density altitude, runway length, aircraft limitations, and initial climb requirements. Generally speaking, more speed is more better, but it has to be balanced with available runway to stop on. The speeds are planned for the worst case scenario: engine failure at V1, then continue the takeoff and climb. More speed on the ground equals more energy for the initial climb.
When I takeoff out of Ft Myers, FL (RSW) the V1 speed is usually pretty high because RSW has a 12,000 ft long runway. Lots of room to stop if needed.
