Your computer has several ports where you can plug in external devices such as printers and modems. These ports come in two flavors: serial and parallel. Usually, your printer plugs into a parallel port. Your modem almost always plugs into a serial port. (However, some new high-speed modems plug into a parallel port.) If you purchase an external modem, you should purchase a modem (serial) cable at the same time.
Since your computer may have multiple ports, we need names to tell them apart. Your first serial port is COM1. If you purchased a second serial port it will be COM2. Your computer can have up to four serial ports.