Codec means "compression/decompression" much in the same way Modem means "modulate/demodulate". The codec is the part that takes a compressed movie file and converts the compressed garbage that makes the file small back into real moving pictures.
Without compression our movie file would be of gargantuan proportions. Compression makes them small without losing (too much!) picture quality.
Each video file has four characters at the beginning of it. This tells your computer what codec it needs. There are lots of programs that tell you what codec you need. Resis the urge to grab ALL of them, just install what you need. They fight otherwise, all trying to compete to decode the stream.
Sometimes your computer will download the correct codec automagically. Sometimes not. I just spent half a day trying to find a codec that will let Windows Media Player play AVI files from a Fuji Finepix A101 camera. I didn't find one (that was free). But the short answer is "Download Quicktime (from apple.com)". That does indeed work.
The AVI files produced by the Fuji camera are encoded with "MJPG" or "Motion JPEG". Many digital camera use this format to squich together many picture to make a video. It's an ok format for grabbing data to use in a video editor program but it's wholly inappropriate for distribution of files, it's way too big. Convert it to an MPG! honest...
There is a very good paper at Cambridge university engineering department that goes into as much detail as you need: