OK, let me expand on codecs. Codecs are a compression algorythm. Look at it somewhat like a zip file and how a zip compresses a file down to almost half the size. This works much the same. For instance; take a Bit Map Image (.bmp file). You will see that there is no compression when working with a bmp. Every dot or pixel is enumerated and given a value. Now take that same file, edit it and save it as a JPEG or .jpg file and all of a sudden a bmp file that is 1.5MB is compressed to a 240K or even smaller JPG. JPEGs are just compressed images, and there are a few other good compression algorythms like GIFs etc. Gifs allow for a small amount of animation, but tend not to be as clear as a JPG which is a static picture and cannot change with animation. This is why these 2 formats are the most used on the Internet because they take less time to download compared to BMPs. Now take a normal music CD. The format in which a CD is burned is a WAV file. A wav file is also an un-compressed bit for bit resemblence of a piece of audio. Now lets take one of the best known audio compression algorythms; the MP3. This is the third revision of MP compression format. So you rip a CD into MP3s. This converts the 60MB WAV file that is on the CD to a compressed format of MP3 which only takes up about 4-6MB instead of 60MB depending on the sample rate you set. I usually set mine to 192Kbps. Granted, compression algorythms are not lossless. Meaning, if you analyzed the audio or video, a person who knows what to look or listen for can notice a slight difference. Usually the higher bit rate that you rip something at like say I ripped a CD at 320Kbps instead of 192Bps, the less a change in the output file is going to be noticed.
Understanding the above, leads me to finally explain what combined audio and video codecs such as DivX. Think of every frame in a video as a BMP and every audio track as a WAV file. Now, rip the audio track down to an MP3 compression. Now take every video frame which is normally a BMP, and compress it to a JPG frame. Synchronize the audio with the video, and you end up with a highly compressed audio/video segment. Take a DVD for instance. You can easily rip a DVD which is normally 7-8GB down to a single 700MB. The more quality you want would then mean you would need to up the bit rate which of course makes the final output file larger. In a nut shell that's pretty much it.
Now there are also some extra things that a Codec also does. Throughout a movie you are bound to have numerous video frames that are the same. DivX and some other codecs take advantage of this by only capturing the frame once and saving it. So say frame # 41, 42, & 43 were the same exact frame or very very similar once analyzed. Instead of encoding 3 JPG files, it encodes 1 JPG file and tells the player to show that frame 3 times in a row. Got it or did I lose you? So what it looks like to the player is a single JPG image #41 X 3 instead of three separate JPG images for 41, 42, & 43.
All different codecs do things a little differently to try and improve performance and quality, hence the need for different codecs on your computer. DivX and XviD (open source version of DivX, and consiquently DivX spelled backwards) are pretty close however, but most of the rest are quite different from each other. Although if you have an XviD codec installed and you play a DivX movie (or vice-versa) sometimes you will find that the audio does not sync up to the frames correctly.
I know it may sound confusing, so if I lost anyone, I would be glad to expand.