Frame rate (also known as fps) is the frequency rate at which a video device produces unique consecutive images called frames. Frames are still pictures that when sequence together form a fluid animation that is the basis for all moving media. Frame rate is most often expressed in frames per second (fps).
Low fps will result in a "choppy" gaming experience, as far as looking like a slideshow in extreme cases. Difficult calculations (like blowing up large amounts of TNT or spawning in a large number of mobs) can temporarily decrease the fps to a complete stop.
Increasing frame rate
Most of the following suggestions are configurable in the game's Options menu, accessible by pressing Esc.
Turn down your render distance.
Set graphics from Fancy to Fast.
Turn off smooth lighting and clouds.
Set particles to minimal.
Set mipmap levels to minimal.
Set the game to small screen mode, as this makes the game load less on screen, making the game run a little bit faster. However for computers which have a better graphics card, change your settings, so Minecraft is in full screen mode, this makes the GPU focus more on Minecraft and less on other programs. Test both ideas and see which setting works best!
Also note, close any programs in the background and close any internet browsers.
If in multiplayer, move away from areas densely populated by players.
Enabling VBOs may result in higher fps.