Pretty well explained by Mr T already. I'll add some of my own rubbish into the mix:
All overdrive, distortion and fuzz effects are - technically speaking - distortion (a deformation of the waveform by clipping off the top part of the wave), but we guitarists like our distortion, so we subdivide them, giving them different names for their different sonic characteristics.
Overdrive - is a smoother sound, more the way a valve amp distorts. It varies in amount depending on how hard you play (play softly, the sound is clean, but the harder and louder you play the more overdrive you get), so is dynamic. It also transitions smoothly from clean to clipped. The clipped wave is rounded off a little to make the sound smoother and "warmer" - called "soft" clipping.
Distortion - is a bit harsher sounding and "rough edged" than overdrive. It clips the waveform more abruptly - called "hard" clipping . Has less playing dynamics.
Fuzz - is the most extreme sounding distortion effect and has no dynamics at all. The clipping is extremely hard turning the signal into a near square wave.
This is what a distorted wave will look like with hard and soft clipping: