This was inspired by the ad copy for an app called SoftSkin Photo Makeup by SoftOrbits, a giveaway on SOS. They hint that using Photoshop layers is, well, bothersome. Truth is, layers are so useful they've been included in Windows Paint, along with quite a few photo editing apps. So, what are layers?...
Every image starts out on a layer, and you can add however many layers on top of it. Each layer starts out completely transparent, but can hold the complete image, part(s) of the image, or, depending on the software, some sort of adjustment you've applied to the image. You can turn any layer on/off, & change the settings if a layer holds an adjustment. A layer can hold the complete image, and because of that, changing the layers beneath it won't have any effect, but otherwise you can add, turn off, or readjust lower layers, and the result will show when you view the top layer. In Photoshop [& several other editing apps] each layer can also have a mask, which selectively blocks whatever is on that layer, so for example you only lighten / brighten a specific part of the photo, say the center.
A mask is the same size as the photo, & at least in Photoshop, is B&W. A selection shows up on the mask as a shape, with the selected area white, & the non-selected area black. Black blocks the layer from applying, and white allows it. Gray also works -- paint on the mask with 50% gray and the layer will apply at 50% opacity. If/when you use a pressure sensitive drawing tablet & stylus [they're cheap - I bought 2 for $25], you can set it so that the harder you press, the darker the paint stroke, so you can fairly easily blend the area you want to apply an adjustment to, rather than have an abrupt edge. You can turn a selection into a mask, & vice versa -- they're pretty much interchangeable, though since you can paint on it, a mask is more useful, especially if you want or need something besides 100% opacity.
Some editing software will let you change the way a layer blends with the layer(s) beneath it. Lets say you removed the background from a photo, leaving you with the subject of the photo on a transparent background the same size as the original photo. Underneath that layer you can have several different backgrounds, and basically see which one you like best by turning all but one of those layers off. This is a simple example that you can do in Windows Paint, and illustrates the basics. But let's say you have some text you'd like to add to the photo. With the text on the top layer, you can change the blending mode and the layer's opacity, leading to all sorts of effects. You can also do stuff like lighten parts of an image, then have it apply to the layers beneath it only when / where it's lighter than the pixels beneath it.
That said, you do Not HAVE to use layers. When you're using layers you can turn off or delete however many layers to get to an earlier point in your editing, starting over. You can save copies of your photo in an editor without layers, and just start working with one of those earlier copies. In photo editing you Very frequently select parts of the photo that you want to alter, say lightening up a face, and only that face. You can save each selection manually, calling it back up whenever you need it, saving you the time and effort of recreating the selection. In Photoshop OTOH you can save selections, &/or have your various selections stored as masks on different layers. And while you can copy/paste whatever onto your photo in an editor without layers, you generally can't go back and shift its position, or vary its transparency, which are both things you can do with layers.
The negative aspects to using layers are one, you usually save you work in the editor's native format to preserve those layers, merging them all together to export a .jpg for example. Two, it's something else to keep track of -- you need to be mindful of which layer you have selected to work with. And third, an image file containing layers can get pretty big, since you're storing lots more data.