Many microcontrollers have an onboard UART/USART. These peripherals are serial ports through which data can be sent to and from the microcontroller.
The problem is that the voltages on these pins is at the same voltage as the other I/O pins on the controller... typically 5V or 3.3V. Talking to a desktop computer requires some kind of adapter. If your computer has a standard RS-232 port (which is becoming more and more rare), you can use a chip such as the MAX232 to convert the low-voltage signals to the +/-12V used by standard RS-232.
If not, you can use a serial-to-USB converter. FTDI pretty much has this marketplace tied up (although Microchip has a competing part nowadays, too). You can buy these cables all over the place for $15 and up. I found this post that refers to this product on DealExtreme.com for $4.40, with free shipping.
Buying this cable is even cheaper than ordering a FT232RL chip and making the cable yourself. Check it out!
(Note: the cable doesn't actually use the FTDI chip, apparently. However, it has the same basic functionality.)