Lets start from the beginning.
Video is made up of series of picture frames; changes from one frame to the other creates movement - rather like the matchstick man flip book. If you flick the pages quickly enough, you see the little man dancing. In PAL video, 25 frames are processed every second. That's a lot of pages in a book
Unlike our flip book, digital video is made up of data and the more data processed, the better quality the video. Unfotunately processing every single frame means the amount of data is HUGE. Lets imagine we scanned in every single page of our matchstick man and saved it as a Bitmap file. We want the video to last 5 mins, so thats 25 * 60 * 60 = 90,000 files. How many pictures do you have on your hardrive? Less than 90,000? Of the pictures you do have, how many are bitmaps? Probably none - they're all JPEG, right?
We can reduce the file size of our scanned images by converting them to JPEG. This discards data that isn't needed to make up the picture, but so that the naked eye can't tell the difference. In practice, and depending on how much "compression" you want, the quality will degrade.
So all of a sudden we've compressed our data and reduced the amount of space on the harddrive - we can discard the data to reduce file sizes. What happens if we then print the JPEG and scan it back in as a bitmap? We get back to the same scenario as before - huge file size.
Now let's compare this to a lossless codec. To compress our video, we can use MPEG. But if we convert BACK from MPEG to a lossless codec, we're actually processing 25 key frames of data every single second. So our data actually goes up. But we won't loose any quality whatsoever. This is usually used during the capture process from RAW, analogue video to ensure you achieve an acurate copy of the original. This AVI is then edited and output as a MPEF etc
You can however trancode to MPEG. This will result in a slight degredation of quality as you'll probably throw away more data. But in your case, it's the best way to go.
So that leaves the question of why is the quality bad. Well, to answer that, I really need to know where you got the video from.