From Unofficial BOINC Wiki
The electronic device that converts digital information received from a computer into tones that can be carried over a normal voice telephone system (phone line) or converts those tones received from the phone line into digital signals. The tones used are all within the normal hearing range of a human. Speeds of modems range from the archaic 300 Baud modems that I used as an early adopter of computers in the home to the current 56K modems of today. Unlike a Digital Subscriber Line either the computer is using the phone, or you are, simultaneous use is not possible. A dial-up modem is the hardware device that is used to establish the Dial-Up Connection through the Internet Service Provider to the Internet itself.
The unpopular sounds made by the modem while it is establishing the connection (a major point in some companies commercials) is how the two modems (yours and the Internet Service Provider's establish the maximum possible connection. Though the modem is rated at 56K, the connection may only support a fraction of that speed due to the limitations of the phone line. Noisy phone lines, long distances from the computer to the phone exchange, etc. all degrade the signal capacity of the line and thereby reducing the quality and speed of the connection itself.