Amplitude modulation of unit step signal
Before the step, the modulation signal is 0, so the output is 0.  After the step, the modulation signal is 1, so the output will be a full amplitude carrier.  This is the same as turning the carrier on from having been off.

Such modulation is called OOK (On/off keying), and is a common way to send morse code.  The carrier is on for the dits and dahs, and off during the spaces in between them.