The first time I encountered layers in Gimp, I found them confusing and a confounded nuisance. However, it takes all of three minutes to learn the basic idea of how they work, and you'll rapidly realise they're a brilliant idea and probably the most useful feature of any image-editing program.
Just regard a layer as a transparent sheet of plastic laid over your original image.
You can draw almost anything you like on it. You can have as many layers as you
like, within reason. You can switch them on or off, to show or hide your extra
artistic input, or vary the transparency of a layer to shade it in. If you made
a small stuff-up, you can erase the mistake without damaging the original image,
and if you made a big stuff-up, why, just delete that layer and start again.
The original image is considered to be a layer too, regard it as the bottom layer. It's a little bit special, in that it can't be deleted.
These commands are from Gimp 2.2 (other versions may have a different menu arrangement):
To create a new layer use Layer - > NewLayer.
To see the list of layers, use Dialogues -> Layers. The menu you get allows you to do all sorts of useful and interesting things with them.
To save the finished work as a bitmap or JPEG or similar, you need to first merge
the layers with Image - > Flatten Image.
If you just select 'Save As' and specify a BMP or JPG, Gimp will prompt you to merge the layers as part of the saving process.
Of course, it also makes sense to save your working copy with all the separate layers as a .XCF file (Gimp's own format) for future use.
Well, that was about 1% of what you can do with layers. This page is just a footnote, so I'm not going to go into any further detail here (besides which, I don't know most if it myself). Hopefully the above will get you started, to go into more detail there's always the Gimp help manual or Google.