What are they; what do they do;
when would I use them; and, how will they benefit my photo doctoring ?Paths are vector lines as explained in Sepiana's link.
Elements has very limited vector handling capacity, mainly selections, shapes and text.
The full Photoshop has more features to work with vectors, and Elements+ gives you back some of those tools.
When are the scripts mentioned by Sepiana useful in your everyday's editing?
First, if you ask Photoshop users what they are doing with paths, they'll tell that they use the pen tools to create a clean 'vector' selection of a part of the image. It's a powerful selection tool, since you can change manually all the 'point's of the vector shape to follow the contours of your subject. You may do a Google search for handling of Bezier curves.
Well, for Elements, forget it. No pen tool, no way to alter flexibly a given path.
For your photo doctoring (you mean editing, enhancing?) you don't need paths.
But if you have a look at the tools provided by Elements+, you'll see that there are interesting possibilities when you deal with selections, shapes and text.
When you are working with vector layers: shapes and text or when you save selections, Elements works internally on paths. Those 'vectors' are not defined by pixels, they are curves defined mathematically. They can be enlarged without pixellisation, they have to be 'simplified' into bitmaps to allow all the other kinds of layer edits of the editor.
Example #1: creating a 'custom' shape.
Elements lets you combine several of the supplied shape library with several options (add, substract, transform...) and to create a new resulting layer shape. No need for additional Elements+ tools.
You can also start with a selection. You have used the existing selections tools to create a rough selection with pixellated contours. You want to save that selection as a shape, to keep the enlarging capacity of vectors and to 'smooth' the contours. The solution is to use the script to transform a selection into a path.
To be able to save the path or the selection, you have to save in the tiff or psd format which keep layers and
paths selections. That way you can reuse that 'custom' shape in a library for use in other images. A common use is to have a custom shape for a personal and flexible logo. When compositing (scrapbooking for instance), that feature is very flexible. Remember that text is also vector and works like a shape.
Example #2: Saving a path in a jpeg
It's a little known property of the jpeg format: you can't save layers, you can't save selections, but you can save a 'clipping path'. That feature is commonly used to save the useful part of your image while knowing you can select the external part you can't make transparent and cut it later on. You can send a jpeg with its clipping path when using a white background is not enough.
By the way, I tried once the feature in this forum and it seems that it strips the path... I'll have to give a link to an external site to give an example.
Example # 3: Watermark challenge
Let's assume you have created a path for your watermark (text only or elaborate shape).
Can you send a jpeg with a 'hidden' watermark that can only be revealed by using the path tools of Photoshop or Elements+ ?