The left one is the 'soft' pedal. It either moves the action so fewer strings are hit by the hammers (on grands) or pushed the hammers closer to the string (on uprights) thereby reducing the piano's volume.
The center pedal varies on different pianos.
On some grands, it is the Sustuneto pedal, which works like the right, sustain pedal, but only sustains the keys being held down when the sustenuto pedal is pressed.
Some pianos, grands and uprights, the center is just like the right pedal except it only sustains the bass section of the piano. A cheaper version of the true sostenuto pedal.
Some modern uprights use the middle pedal as a super-soft pedal. The pedal lowers a strip felt between the hammers and the strings, making the piano very soft indeed.