It's about non destructive editing, a very powerful tool for professional workflows especially for fine tuning changes and making things repeatable.

Once you have worked with them, you won't want to work without them.

and yet I've worked without them just fine for 15 years or more

For instance - in Photoshop, one can add an adjustment layer on a picture that alters the saturation and color balance of that image. One can then copy that layer for use later, or edit that layer on the fly if one decides it's not right. Or delete it entirely, much later in the editing process.