A serial port is the socket (also known as an "input/output connector") where you plug in the cables to attach to a serial device, such as a printer or modem.
Data is transmitted through a serial port in a single file, one bit at a time, but there are two data wires so a serial port can send and receive information simultaneously. Parallel ports connect with cables that have parallel wires so they can transmit data faster; they accommodate eight bits of data at a time (on a pc, however, parallel data can only flow in one direction at a time).
Most Macintosh printers are serial printers, though the bulk of those use the Mac's LocalTalk network port. While technically a serial port, LocalTalk is much faster and more complex than the serial port used for modems and other serial printers like the Image Writer. LocalTalk is generally faster than the parallel ports on pcs, though the standard Mac serial ports are slower. The slower rate of the standard serial ports is not really a problem since non-LocalTalk serial printers take much longer to process the information anyway than the computer takes to send it.
Because the two platforms (Macintosh computer systems and IBM computer systems) each use a different sort of port to connect to a printer, they can't share the same printer without some sort of adaptation (or unless the printer is designed to support both platforms simultaneously).