This process is called modulation. The analog signals are sent across your phone lines, through the telephone company's switching equipment, and then converted back into digital data by the receiving modem. This end conversion is called demodulation. Your computer speaks in an all digital 'language'. A modem is fed digital information by your computer in the form of ones and zeros, from the CPU, through your computer's serial port or ISA slot.
Computers are digital by nature.
The phone line is where the bottleneck occurs. POTS lines are only suited to carry a small amount of bandwidth . Bandwidth is a technical term for the amound of 'headroom' on a given telecommunications medium. This is roughly enough for about 31,200 bits per second . Since the amount of bandwidth on a voice telephone line is limited, the amount of information you can get in a given period of time is somewhat constricted.