The average volume level of an audio signal over a short period of time, or a control signal representing the volume level. Non-synthesizer instruments tend to fall into one of two categories: Struck- and plucked-string instruments (piano, harsichord, guitar, etc.) tend to produce a sharp attack transient, followed by a gradual decay of the sound until it fades to nothing, or it might be possible for the performer to mute the note before it fades out. Bowed-string and wind instruments tend to have a more or less "on-off" characteristic, where the note starts, remains at more or less the same level for as long as the performer wants, and then stops when the performer quits exerting effort to sustain the note.
The envelope generator in a synthesizer is designed to imitate these two types of envelopes, as well as produce many more, with varying levels of subtlety. The most basic type of envelope generator, the AR generator, will produce a signal that starts from a zero level when a key on the synth is played, rises to a maximum level, and then falls back to zero. The rise portion is the attack, and the fall portion is called the release, the envelope generator will provide controls for controlling the attack and release times. This type is adequate for producing a basic percussive envelope, but for sustaining notes, the envelope generator will add at least a sustain phase. After the attack phase, the generator will go into the sustain phase, at which the envelope signal remains at the maximum level, and remain there for as long as the performer holds down the key on the keyboard. When the performer releases the key, the generator goes into the release phase. A more sophisticated type commonly found on synths is the ADSR generator, which adds an additional decay phase that comes immediately after the attack phase and precedes the sustain phase. This generator provides two additional controls, one for the decay time, and another for the level that is held in the sustain phase.
Since many of the audio signal sources that are used in synths produce a signal all of the time, the signal is routed to a voltage controlled amplifier (VCA), which controls the signal level. The envelope generator produces the control signal for the VCA, which causes the VCA to shape the note envelope as the performer desires. (Which includes fading out the signal at the end of the release phase, so that the note doesn't sound all of the time!) This is the most common use for an envelope generator, but do note that envelope generators have many other uses.
One other envelope-related circuit found in synths is the envelope follower. This circuit extracts a control signal representing the envelope of an input audio signal. By routing the signal produced by the envelope follower to a VCA, a synth signal can be made to follow the dynamics of, say, an acoustic instrument that is mic'ed up and input to the envelope follower.