The modem is a device that enables the PC to use a telephone line to communicate with other PCs, devices and the Internet. The name comes from "MOdulation DEModulation".
The modem plugs into a slot on the motherboard or is incorporated directly into the electronics of the motherboard. It converts data into signals that can be transmitted over the telephone line and receives data to convert back for the PC to use.
The modem speed refers to number of bits of information it is capable of transferring per second. A 56K modem is capable of transferring up to 56,000 bits of information per second. In reality, a 56K modem maxes out at about 50K because of FCC limitations. Furthermore, telephone line noise and other issues can result in even lower transfer speeds.
A hardware modem includes circuitry directly on the modem to handle the modulation and demodulation process. A software modem transfers the work to the CPU. A hardware modem is more expensive but it frees up the CPU to work on other tasks, thus improving overall performance.
While modems were once standard in new PCs, for their use for a connection to the Internet, they are becoming less commonplace. While some still use dial-up access to the Internet, DSL & Cable have substantially replaced that service. Modems most common use is now for fax transmission.