An envelope is a four-stage process that sounds travel through over a period of time. The four stages are known as Attack, Decay, Sustain and Release (ADSR). Envelopes help you to create expression and character within your sounds.
If you think of a graph with the X-axis representing time and Y-axis representing the volume, each stage can be plotted on the graph at high or low points to create a dynamic sound that changes over time.
Attack describes the amount of time the envelope takes to reach the maximum volume. This could be instant or a gradually rising sound.
Decay relates to the amount of time the sound takes to drop from the maximum volume down to the sustain stage.
Sustain is the level of volume that the note is held at, it is not a measure of time and could, therefore, be maintained indefinitely.
Release describes the amount of time it takes for the sound to drop back to zero after key release or the sustain has ended.
Without envelopes, your sounds would hold no character. For example, hitting a key on the keyboard would create a sound at maximum volume and it would stay there until you release the key. No fade-in, no fade-out, and no dynamism.
Envelopes are most commonly used with amplified modulation (changing the sounds volume), but they can also be used to modulate other parameters such as the cut-off frequencies of low pass filters and pitch variations. Envelopes are key to creating unique synthesizer sounds.