Most online sites that allow for varying video quality store their videos in tiny pieces. This is so the video can get better or worse as soon as possible to give the most appropriate quality for your connection.

Downloading the little files and putting them all togeher is the only way to download these videos, so that's what LetMeAtIt does. The status will tell you how many files are being downloaded and the progress bar shows how far along it is.

After these have been downloaded, then they are joined together into one big whole and then (usually) converted to MP4. The little files will then be deleted.

You won't be left with having to watch the tiny files, just wait a bit longer and you'll have one big file (which is much easier to watch :-)