When most people use the term "serial port" they're referring to a DB-25 or DE-9 port you find on older computers or USB dongles. It's also seen in 8P8C (aka "RJ45") form sometimes, especially in industrial equipment. It can send and receive "characters" (anywhere from 5-8 bits each) one at a time at a fixed rate, either half duplex or full duplex. They usually implement one or more of the RS232, RS422, or RS485 standards.
Originally, you communicated with the computer using a teletype or video terminal connected to a serial port. Whatever you typed went to the computer, and whatever the computer sent back was printed on your terminal screen (or paper in the case of a teletype).
The UNIX (and thus, Linux) command line environment still works this way, except the serial line is virtual.
It is a port that has two data lines, RX and TX, and data is sent in a serial fashion across those data lines. It is used today for embedded systems, routers and switches et al, and getting a console on any machine that doesn't have a gpu with a monitor attached.
USB is a serial BUS, which allows multiple devices; serial ports are single device (if my memory serves).
