A control signal that, when received by a synth, causes notes that are being held on the keyboard to continue to sound after the performer releases the keys. Specifically, on synths with conventional envelope generators, it causes the gate signals associated with the held keys to remain in the active state, which will cause the envelope generators of the associated voices to remain in the sustain phase. When the sustain pedal signal goes inactive, the envelopes for the voices being held go to the release phase.
A sustain pedal usually takes the physical form of a small, spring-loaded footswitch that connects to a jack on the rear of the synth. The sustain pedal function is active as long as the physical pedal is held down. It is vaguely analogous to the sustain pedal of a piano, although the sustain pedal of a piano cannot cause notes to continue sounding indefinitely; the sustain pedal on the synth can, depending on the envelope generator settings. MIDI also allocates a continuous controller message for the sustain pedal, type number 64, and most MIDI-capable synths will send this message when a plugged-in pedal switch is pressed or released.
Polyphonic synths may have different rules for how voice stealing effects notes that are being held via a sustain pedal, vs. notes that are actually being held on the keyboard.
One some Sequential Circuits synths, pressing the sustain pedal or receiving a MIDI Sustain On message activates a mechanism called alternate release, which may sustain the notes, or trigger some other envelope behavior.
Roland synths are notorious for requiring "normally closed" sustain pedal switches, where most other manufacturers used "normally open" switches. The effect is that when a Roland footswitch is used with another brand, or another brand of footswitch is used with a Roland, the effect of the pedal is backwards; it holds notes when not pressed, and releases them when pressed.