The serial port is somewhat obsolete (and often called a "legacy" device, but it's still important, especially for Linux. The serial port has many shortcomings but most new PC's (except for laptops and Macs) seem to come with them. Some PC's, called "legacy-free" don't have serial ports. Linux supports ordinary analog modems only if they work thru a serial port (although the port may be built into the modem).
The physical serial port on the back of a PC, must pass data between the computer and an external cable. Thus it has two interfaces: the serial-port-to 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 EIA-232 serial port is inherently low speed and is severely limited in distance. Ads often 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 a network card, even this "high speed" is actually low speed. All of the EIA-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 EIA-232 is. See Successors to EIA-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 115 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, Firewire, etc.
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. The ISA bus is usually 16-bits wide and the efficiency is intermediate as compared to efficient LPC and inefficient PCI.