To me, Adobe Photoshop Elements is something like the little brother of Photoshop. It's not as abundant in what it lets you do, but the features it does have, it makes its own.
Photoshop Elements looks exactly like regular Photoshop at first glance. The interface design is basically the same, and if you have any experience with Photoshop, you will feel right at home. There are, of course, fewer features and options available, for example, color models are unavailable when editing a picture, restricted work modes for some tools are absent, and you can't work with separate channels, some filers are missing, etc. Hence the title of the little brother of Photoshop - it does most of the same, but doesn't do all.
However, Photoshop Elements has its own advantages. The Cookie Сutter tool can be used to cut very specific parts and figures out of a picture in an advanced mode. There's also the Smart Brush, a tool to apply effects with a brush. Photomerge includes new features for combining several pictures. It even has nice little things like automated file splitting.
Finally, Photoshop Elements includes social media integration. Users can share edited pictures and post them on social networks.
Basically, Adobe Photoshop Elements is the right tool for people who want to use Photoshop, but don't want to deal with its price and difficulty.