A "catch-all" mailbox is a server-side setting so that any unknown email addresses for my domain get delivered to a named mailbox.
For example, on my domain "anything-goes-here(at)my.domain.uk" (not my real domain) gets delivered to the predefined account "anon".
When I provide an email to register on a website, I enter something unique to that website and it gets delivered to the "anon" account, and AquaMail correctly shows the original address it was sent to.
This way if a website gets hacked, or they sell my address to third party marketing companies, I know which organisation sold it and can block them by changing that address on my email server to redirect to my spam account. It's like having a wildcard rule on the server that delivers any mailbox name to a specific account.
The only issue is if I have to reply to one of those emails, the from-address (or reply to) is not automatically set to the address the mail was sent to, but is from "anon(at)my.domain.uk"
Does that explain it better?