1995 Toyota Camry Car vibrates at higher speed

I hv 1995 Toyota Camry. It has approx. 100,000 miles on it. The car starts vibrating above 60 mph. Higher the speed, higher the vibration. This problem started just some time back. When I hold the steering, I can feel my hand vibrating too much. Even the persons sitting on the passenger seat can realize very easily that the car is vibrating. On lower speed, the car runs absolutely fine. Can you please suggest might be the problem. I went to one of the car mechanic and I feel that he tried mis guiding me, as per him the rotors of the break needs to be replaced. I really can't understand what rotors of the break has to do while the car is running and having vibration because of a higher speed. I'll really appreciate your kind advice on this. Thanks and God Bless.