Most synthesizers use an envelope composed of four sections: attack, decay, sustain and release. Roughly speaking, the attack affects the beginning of the sound, followed in order by the other three sections. For example, a short attack setting on the sound's volume envelope causes it to start playing abruptly, while a longer attack setting makes the sound gradually swell up. A long release setting on the volume envelope causes the sound to gradually fade away; with a short release setting, the sound stops playing as soon as the input to the synthesizer stops.
Depending on the specific model, a synthesizer can use envelopes to modulate, or alter, nearly any aspect of a sound. The amplitude envelope controls the volume of the sound, while the filter envelope determines the degree to which the synth applies the filter to each section of the sound. Modulation envelopes are configurable, meaning that you can assign them to alter one of several parameters on the synthesizer. For example, assigning the modulation envelope to the sound's pitch, then increasing the envelope's sustain and release, creates a sound that goes down in pitch as it fades away.
Although the ADSR envelope structure is the most common, more advanced synthesizers can use more complex envelopes to modulate a sound. Some synths add a "hold" section to their envelope generator; others split the decay into multiple sections. The more complex the envelope, the more control you have over the sound; however, more complex envelopes also involve a steeper learning curve. Certain software synthesizers are capable of extremely complex envelope settings.
Digital audio workstation programs use the term "envelope" in a broader sense to refer to any configurable parameter that changes over time. You can, for example, draw an envelope onto a MIDI clip to change its pan setting over time, or to gradually increase the degree to which the program sends the track to a return channel. This type of envelope can be much more complex than the typical ADSR envelope, and can apply to a whole series of notes, rather than to just one sound.