Before Adjustments Layer were introduced photographers would have to duplicate the background layer to avoid editing or damaging the original image. While you can still do this, Adjustments layer allow you to apply adjustments like curves, Levels or hue/saturation as a separate layer that you can refine, changes or delete at any time during your editing process. The alternative would be to apply an adjustments command via Image>Adjustments directly to a duplicate image layer, but this won't give you the flexibility of editing the effect after you have committed to it. Plus, if you want to get rid of the adjustment's effect, you will have to delete the whole image layer, which can be frustrating if you have applied the different adjustments to the image layer you need to delete it.
Most of the usual Adjust command is available as an
adjustment layer making it a much more favorable way to edit the picture, but it's still worth checking out the adjustments menu for those commands you cant access as a separate layer. Being able to control how an adjustment affects your image post-application means you are not committed to any adjustment command you use, making the process a lot more forgiving and fluid. Not only you can reverse or delete an-adjustments, you can temporarily hide them the same way you would an image layer, you can apply a blending mode or fine-tune the effect by changing the opacity and you can restrict the effect using the layer mask.
An Adjustments layer can be created in one of the three ways: by clicking Layer>New Adjust Layer and selecting your required adjustments, clicking on the adjustments icon (Half black/half-white circle) at the bottom of the layers palette to access the same list of options or by opening the adjustments panel via the window menu. Any of those work, but some are quicker than others and offer you more options: You just need to find the one you work with the most efficiently.