Why In amplitude modulation the RF carrier's amplitude rises and falls in step with the modulating audio. If you trace a line through the tips of the successive RF cycles, that outline reproduces the shape of the modulating waveform, and that outline is what is called the modulation envelope. An oscilloscope display of an AM signal shows this envelope directly, which is why you can spot overmodulation (flat-topping or pinching off at the zero line) by watching it.
Watch out Calling it the bandwidth confuses the envelope with occupied spectrum: bandwidth is a frequency-domain measurement, while the envelope is a time-domain shape. The carrier itself is just the constant-amplitude RF being modulated, not the outline traced by the peaks.
Envelope = the outline you'd draw around the RF peaks on a scope, and it looks like the audio.