Simply put, layers are images stacked on top of each other.
Layers are mostly used in combination with a reduced opacity so that elements of the images behind are shown by transparency.
When to use:
Layers can be useful to emulate particle effects or to blend different images.
Oftentimes you will also benefit from duplicating layers in Gimp so that you can apply different settings to them while preserving the original one.
Mostly, layers are a convenient way to work with multiple images and to blend them with a sense of depth.
Try putting a layer simply filled with one color on top of your photo, then blend it down with a soft or hard light and notice how it changes the image. You can in this way in effect change the dominant color and style of your photo, while brightening or darkening it at the same time.
Blending simple layers becomes most powerful when used with the dodge and burn masking technique.