The thumbnail cache is a critical piece of the engine that powers the Photo Browser. It takes time -- up to several seconds -- for the software to read a high-resolution image file and create a small version of the image to display in the Photo Browser. If Elements were to simply read the high-resolution file for each photo and create thumbnails "on the fly" as you scroll the Photo Browser, scrolling would be intolerably slow.
To enable fast scrolling, Elements stores small versions of each photo in a file called the thubmnail cache. Once a thumbnail file is stored in the cache, the software can just fetch this thumbnail when it needs to display it. New photos are added to the thumbnail cache only when they are needed for display. Eventually, you'll have copies of every photo in your catalog in several sizes stored in the cache. This file can grow very large; it is typically much larger than the catalog file.
In normal operation, you don't have to deal with the thumbnail cache explicity; it works behind the scenes. (See page 111 in Organize Your Photos with Adobe Photoshop Elements 3 for more details on how the thumbnail cache operates in normal operation.) Under rare circumstances, however, the thumbnail cache can become corrupted. When this happens, Elements may fail when it tries to start the Organizer, or you may see thumbnails in the Photo Browser that don't correspond to the right high-resolution file.
There is no way to repair a corrupted thumbnail cache, so you just have to get rid of it. Fortunately, Elements will simply make a new, empty thumbnail cache and start filling it up. All thumbnail cache files are named tn.4.cache. In the folder C:\Documents and Settings\All Users\Application Data\Adobe\Catalog Folders you will find a folder for each catalog that you've created, named with the name of the catalog. In each catalog's folder is a tn.4.cache file. If you want to start fresh with a new thumbnail cache, exit Elements, rename the tn.4.cache file to something like tn.4.cache-old (so you can retrieve it later if it turns out it was not the source of your problem), and restart Elements, which will create a new tn.4.cache file. Once you've certain that you don't need the old one, delete it.
Because photos are added to the thumbnail cache only as they are needed for display, you have to sit through a lot of very slow scrolling if you start with a fresh thumbnail cache and just wait for it to get filled up on demand. Instead, select all the photos (pressCtrl-A when the Photo Browser is showing all your photos) and choose Edit > Update Thumbnail. Elements will then fully populate the thumbnail cache, which can take hours for a large catalog. If you have more than a few hundred photos, take a coffee break -- or a lunch break -- while this process runs. If you have many thousands of photos, start the process at the end of the day and let it run overnight.