how would you explain 404 error to a client?

I use the shop analogy - the shop's open, that one shelf is gone. Then the part they actually need to decide: if the old page had links or traffic, redirect it to the closest replacement. If it didn't, leave it as a 404, nothing is broken.

Nothing exists at that address - the site is fine, that one page isn't. It only really matters when the address used to work, because then links are still pointing at it.