It's quite an interesting topic

If you monitor/TV is 60 Hz, it shows 60 frames per a second.

This means a frame is on for 1/60 s, which is ~17 ms

For 30 fps a frame is on for 1/30 s, which is ~34 ms

For 120 fps a frame is on for 1/120 s, which is ~8 ms

So the latency basically halves going from 30 fps to 60 fps to 120 fps

Which is why increasing the frame make the game much smoother

Also there is also the monitor/TVs response time to take into account

Your average monitors/TV would add another 5-10 ms, a gaming monitor would be about 1 ms.

Was the difference is much more noticeable in first person shooters, where slow reactions get you killed

http://30vs60.com/

http://boallen.com/fps-compare.html

http://gfycat.com/MerrySpiritedBass

http://gfycat.com/OblongTautDragonfly