Multiplexing is the process in which several channels are combined n such a manner that they can be transmitted through a single channel.
But what’s Charlieplexing?
Charlieplexing has almost the same idea. But here it is for driving LED’s from less number of pins .
So whats the use of this technique?
You can drive a large number of LED’s from a less number of pins. You might be saying that it is possible using a multiplexer.The answer is not wrong. But it will be hard for a huge number of LED’s.
See this example http://home.wanadoo.nl/electro1/avr/kitt.htm
See the explanation in Wikipedia
” Charlieplexing is an electronics technique developed by Charlie Allen (hence the name) at Maxim in which relatively few I/O pins on a microcontroller are used to drive a large number of LEDs.
With Charlieplexing, n drive pins can be used to drive n digits with n-1 segments each; in other words, n drive pins can be used to control n2-n LEDs. Traditional multiplexed display technique would take 2n drive pins to control n2 LEDs.
Charlieplexing works by having the I/O pins alternate between driving digits and driving segments.”
See a sample circuit of controlling 56 LED’s through 8 pins

You can find more info fron the wiki page for Charlieplexing
Check these for more
http://www.instructables.com/id/Charlieplexing-LEDs–The-theory/
http://www.instructables.com/id/How-to-drive-a-lot-of-LEDs-from-a-few-microcontrol/


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