A serial port is any physical communications port over which data is transmitted serially rather than in parallel, but most often is is used to refer more specifically to the RS-232 port on a computer or other device. The RS-232 standard was first published in 1962 and was originally intended to standardize the connection between Data Terminal Equipment (DTE) and Data Communication Equipment (DCE). At that time a typical DTE was a teletypewriter and a typical DCE was a modem.
Since that time, a great many devices have used and continue to use this kind of serial communications. Physically, serial communications is minimally three lines: RX (receive), TX (transmit) and GND (a common ground connection), but many serial port implementations included more than this minimum complement.