What is the modulation envelope of an AM signal?

In Amplitude Modulation (AM), the information (such as a voice signal) is used to continuously vary the amplitude of a high-frequency carrier wave. If you were to view this modulated signal on an oscilloscope, you would see the carrier wave's peaks rising and falling in time with the audio. The 'modulation envelope' is the boundary or outline formed by tracing an imaginary line across the tops of these rapidly changing carrier peaks. This outer shape is an exact visual replica of the original modulating audio waveform. Distractors in this question try to confuse this visual time-domain shape with frequency-domain concepts. The envelope is not the bandwidth, nor is it related to spurious signals 'enveloping' nearby frequencies.