The serial port used to be found on almost all new PC's but not anymore. Thus as of 2008, it's becoming obsolete, if not already obsolete. It's often called a "legacy" device, but it's still used by some for hardware designed to connect to the serial port especially for computers used as servers by companies. Laptops and Macs stopped being sold with serial ports several years before desktops did. However, if one needs a serial port, it's possible to buy one and install it, such as on the USB bus, and it's still found on older PC's. Linux supports ordinary analog modems only if they work thru a serial port (although the port is likely to be built into the modem) so a PC often has a serial port even if you can't find any serial port connector on the back of the PC.
The external serial port connector on the back of a PC, must pass data via an external cable connected to that connector. Thus it has two interfaces: the serial-port-to-external-cable and the serial-port-to-computer-bus. Both of these interfaces are slow. First we'll consider the interface via external cable to the outside world.
The conventional RS-232 serial port is inherently low speed and is severely limited in distance. Ads used to read "high speed" but it can only work at "high speed" over very short distances such as to a modem located right next to the computer. Compared to other connections to a PC such as as a USB bus, network card ethernet, or IEEE 1394 (firewire), this claimed "high speed" for a serial port is actually low speed. All of the RS-232 serial cable wires use a common ground return wire so that twisted-pair technology (needed for high speeds) can't be used without additional hardware. More modern interfaces for serial ports exist but they are not standard on PC's like the RS-232 is. See Successors to RS-232. Some multiport serial cards support them.
It is somewhat tragic that the RS-232 standard from 1969 did not use twisted pair technology which could operate about a hundred times faster. Twisted pairs have been used in telephone cables since the late 1800's. In 1888 (over 120 years ago) the "Cable Conference" reported its support of twisted-pair (for telephone systems) and pointed out its advantages. But over 80 years after this approval by the "Cable Conference", RS-232 failed to utilize it. Since RS-232 was originally designed for connecting a terminal to a low speed modem located nearby, the need for high speed and longer distance transmission was apparently not recognized. The result was that since the serial port couldn't handle high speeds, new types of serial interfaces were devised that could: Ethernet, USB, IEEE 1394, etc. All of these use high speed twisted-pair cabling as recommended by the "Cable Conference" of 1888.
The serial port communicates with the computer via the PCI bus, the LPC bus, X-bus, or ISA bus. The PCI bus is now 32 or 64 bits wide, but the serial port only sends a byte at a time (8 bits wide) which is a waste of PCI bus bandwidth. Not so for the LPC bus which has only a 4-bit wide bus and thus provides an efficient interface even though it takes two transmissions to send a byte. The ISA bus is usually 16-bits wide and the bus utilization efficiency is intermediate as compared to efficient LPC and inefficient PCI (although ISA is overall less efficient due to it's lower speed).