Anything involving masking, layers and compositing, e.g. switching in a new background or sky; removing unwanted people in your shot; merging two or more photos into one; and so on.
Pixel-level stuff like removing lots of scratches and blemishes; adding special filters to give artistic effects; overlaying text and shapes, etc.
And then there are the special tricks like recomposing a shot to bring, say, a couple of people closer together while compressing the background but without compressing the people (has to be seen in action); fixing keystoning of, e.g. buildings; shortening depth of field to get nice portrait shots; creating special effects like Out of Bounds or reflections; getting the best smiley faces in a group of shots and merging them into one shot.
In my opinion, it's well worth the money you pay for it. There's so much you can do with it that you just can't do in LR. And it integrates with LR nicely so that you can right-click a thumbnail and click "Edit in Photoshop Elements", do your editing, save and exit back into LR with your editing changes intact.
A Google search for "compare lightroom and elements" will tell you more.