Email verification
Email verification is checking whether an address can actually receive mail before you send to it. A full check tests the syntax, then the domain's mail records, then asks the receiving server about the specific mailbox.
The word covers four checks of wildly different strength, which is why two providers can both sell "verified emails" and deliver very different bounce rates. The weakest is a format check, which only proves the address is shaped like an address. Then a domain check, then an MX record lookup, and only the last step — an SMTP probe against the receiving server — says anything about the mailbox itself.
Even a full probe cannot always give a yes or no. Plenty of servers accept mail for every address at the domain, so the honest answer there is neither valid nor invalid, and a verifier reporting them as valid is guessing on your behalf.
The reason to care is that bounces are the fastest way to damage a sending domain. Mailbox providers read a high bounce rate as evidence you are sending to a list you did not collect yourself, and the reputation damage carries over to every message you send afterwards, including the ones people asked for.
Goes deeper: Email Verification, Explained Properly