A sustain pedal or sustaining pedal (also called damper pedal) is the most commonly used pedal in a modern piano. It is typically the rightmost of two or three pedals. When pressed, the sustain pedal "sustains" all the damped strings on the piano by moving all the dampers away from the strings and allowing them to vibrate freely. All notes played will continue to sound until the pedal is released.
This lets the pianist sustain notes which would otherwise be out of reach, for instance in accompanying chords - and accomplish legato passages (smoothly connected notes) which would have no possible fingering otherwise. Raising the damper pedal also causes all the strings to vibrate sympathetically with whichever notes are being played, which greatly enriches the piano's tone.
Read more about Sustain Pedal: History, Specifying Pedaling in Musical Compositions, Sostenuto Pedal, Other Instruments
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