UARTs (Universal Asynchronous Receiver Transmitter) are serial chips on your PC motherboard (or on an internal modem card). The UART function may also be done on a chip that does other things as well. On older computers like many 486's, the chips were on the disk I/O controller card. Still older computer have dedicated serial boards.
The UART's purpose is to convert bytes from the PC's parallel bus to a serial bit-stream. The cable going out of the serial port is serial and has only one wire for each direction of flow. The serial port sends out a stream of bits, one bit at a time. Conversely, the bit stream that enters the serial port via the external cable is converted to parallel bytes that the computer can understand. UARTs deal with data in byte sized pieces, which is conveniently also the size of ASCII characters.
Say you have a terminal hooked up to your PC. When you type a character, the terminal gives that character to it's transmitter (also a UART). The transmitter sends that byte out onto the serial line, one bit at a time, at a specific rate. On the PC end, the receiving UART takes all the bits and rebuilds the (parallel) byte and puts it in a buffer.
There are two basic types of UARTs: dumb UARTS and FIFO UARTS. Dumb UARTs are the 8250, 16450, early 16550, and early 16650. They are obsolete but if you understand how they work it's easy to understand how the modern ones work with FIFO UARTS ( late 16550, 16550A, 16c552, late 16650, 16750, and 16950).
There is some confusion regarding 16550. Early models had a bug and worked properly only as 16450's. Later models with the bug fixed were named 16550A but many manufacturers did not accept the name change and continued calling it a 16550. Most all 16550's in use today are like 16550A's. Linux will report it as being a 16550A even though your hardware manual (or a label note) says it's a 16550. A similar situation exists for the 16650 (only it's worse since the manufacturer allegedly didn't admit anything was wrong). Linux will report a late 16650 as being a 16650V2. If it reports it as 16650 it is bad news and only is used as if it had a one-byte buffer.
To understand the differences between dumb and FIFO (First In, First Out queue discipline) first let's examine what happens when a UART has sent or received a byte. The UART itself can't do anything with the data passing thru it, it just receives and sends it. For the original dumb UARTS, the CPU gets an interrupt from the serial device every time a byte has been sent or received. The CPU then moves the received byte out of the UART's buffer and into memory somewhere, or gives the UART another byte to send. The 8250 and 16450 UARTs only have a 1 byte buffer. That means, that every time 1 byte is sent or received, the CPU is interrupted. At low transfer rates, this is OK. But, at high transfer rates, the CPU gets so busy dealing with the UART, that is doesn't have time to adequately tend to other tasks. In some cases, the CPU does not get around to servicing the interrupt in time, and the byte is overwritten, because they are coming in so fast. This is called an "overrun" or "overflow".
That's where the FIFO UARTs are useful. The 16550A (or 16550) FIFO chip comes with 16 byte FIFO buffers. This means that it can receive up to 14 bytes (or send 16 bytes) before it has to interrupt the CPU. Not only can it wait for more bytes, but the CPU then can transfer all 14 (or more) bytes at a time. Although the interrupt threshold (trigger level) may be set at 8 instead of 14, this is still a significant advantage over the other UARTs, which only have 1 byte buffers. The CPU receives less interrupts, and is free to do other things. Data is not lost, and everyone is happy.
While most PC's only have a 16550 with 16-byte buffers, better UARTS have even larger buffers. Note that the interrupt is issued slightly before the buffer get full (at say a "trigger level" of 14 bytes for a 16-byte buffer). This allows room for a few more bytes to be received during the time that the interrupt is being serviced. The trigger level may be set to various permitted values by kernel software. A trigger level of 1 will be almost like a dumb UART (except that it still has room for 15 more bytes after it issues the interrupt).
If you type something while visiting a BBS, the characters you type go out thru the serial port. Your typed characters that you see on the screen are what was echoed back thru the telephone line thru your modem and then thru your serial port to the screen. If you had a 16-byte buffer on the serial port which held back characters until it had 14 of them, you would need to type many characters before you could see what you typed (before they appeared on the screen). This would be very confusing but there is a "timeout" to prevent this. Thus you normally see a character on the screen just as soon as you type it.
The "timeout" works like this for the receive UART buffer: If characters arrive one after another, then an interrupt is issued only when say the 14th character reaches the buffer. But if a character arrives and the next character doesn't arrive soon thereafter, then an interrupt is issued. This happens even though there are not 14 characters in the buffer (there may only be one character in it). Thus when what you type goes thru this buffer, it acts almost like a 1-byte buffer even though it is actually a 16-byte buffer (unless your typing speed is a hundred times faster than normal). There is also "timeout" for the transmit buffer as well.
Here's a list of UARTs. TL is Trigger Level
The obsolete ones are only good for modems no higher than 14.4k (DTE speeds up to 38400 bps). For modern modems you need at least a 16550 (and not an early 16550). For V.90 56k modems, it may be a several percent faster with a 16650 (especially if you are downloading uncompressed files). The main advantage of the 16650 is its larger buffer size as the extra speed isn't needed unless the modem compression ratio is high. Some 56k internal modems may come with a 16650 ??
Non-UART, and intelligent multiport boards use DSP chips to do additional buffering and control, thus relieving the CPU even more. For example, the Cyclades Cyclom, and Stallion EasyIO boards use a Cirrus Logic CD1400 RISC UART, and many boards use 80186 CPUs or even special RISC CPUs, to handle the serial I/O.
Most newer PC's (486's, Pentiums, or better) come with 16550A's (usually called just 16550's). If you have something really old the chip may unplug so that you may be able to upgrade by buying a 16550A chip and replacing your existing 16450 UART. If the functionality has been put on another type of chip, you are out of luck. If the UART is socketed, then upgrading is easy (if you can find a replacement). The new and old are pin-to-pin compatible. It may be more feasible to just buy a new serial board on the Internet (few retail stores stock them today).