Here's an example of video that's available both in the regular version (320x240) and in a higher quality encoding (448x336). The audio is now encoded at a sample rate of 44100 Hz, up from 22050 Hz. As you can see in the screenshots below, the right image is clearer and more detailed.
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While this increase of resolution might seem minor, for the example above YouTube's re-encoded FLV file is more than twice bigger than the old one (from 9 MB to 22 MB), so it will load much slower.
If you append &fmt=18, YouTube downloads the video as a MP4 (H264 with AAC audio), encoded at 480x360. Here's the same video encoded as MP4.
To make things easier, there's a Greasemonkey script that automatically adds the magic parameter for you.
Related:
A discussion about the technical details