Answer
If you look at HSW article on CDs, it talks about how you can store sound digitally. In a digital answering machine these same principles are used to convert a caller's message into a stream of bytes. A microcontroller digitizes the caller's voice using an analog-to-digital converter and stores it in low-power RAM (Random Access Memory).

So let's say a caller leaves a 15 second message. That might translate into 30,000 bytes of digitized data. These bytes are stored at a specific address in RAM (see the HSW article on C pointers for a discussion on memory addresses). To play the message back, the microcontroller reads the 30,000 bytes from RAM and plays them through a D/A converter.

RAM is a high-speed memory device, so the microcontroller can erase one of the messages and easily move the other messages forward into the freed space.

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