Cutting out means isolating a subject from its background so you can reuse it elsewhere (composites, transparent backgrounds, product catalogues and so on).

The modern method

1. Select the subject with the Object Selection tool.
2. Click Select and Mask to refine the edges.
3. Use the « Refine Edge » brush on hair or fur.
4. Output the result to a layer mask.

Why use a mask

Rather than erasing the background (destructive), the mask hides it: you can always go back.

Key point: never delete a background with the eraser. A clean cut-out always goes through a mask.