Stop bits are a way for a computer to "catch its breath" while sending or receiving data, while still letting the other end know that the connection is still there and is still valid; they're also used in error detection.
Stop bits are rather like parity bits. They are sent with the data, but they are not part of the data. Unlike parity bits, they are not turned on and off by the number of bits in the data; instead, they are always on. If one or more of the stop bits are missing, it constitutes a framing error.
Some computers also use start bits for a similar purpose; however, that is not as common a practice as it used to be.
The number of stop bits generally increases with higher baud rates. At 300 baud, usually 0 or 1 stop bits are used. At 1200 baud, 1 or 2 stop bits are most common.
If you connect with another computer and everything seems to be correct, but you cannot read the material you're receiving, one of three possible problems is likely. Either the baud rates are set wrong, the parity is wrong, or the number of stop (or start) bits is incorrect. If the baud rate is correct and the errors are framing errors, it is probably the number of stop bits.
Parity and general error checking
Opening a communications port
Reading and writing data