Double opt-in (also called confirmed opt-in) sends a confirmation email immediately after signup, and only adds the address to the actual sending list once the recipient clicks to confirm. Single opt-in adds the address immediately on signup with no confirmation step.
The confirmation step filters out mistyped addresses, addresses entered by someone other than their owner, and bot-submitted signups, all of which are common sources of spam-trap hits and elevated complaint rates under single opt-in.
Double opt-in also produces a clear, timestamped consent record, which is useful evidence for consent-related compliance obligations, separate from whatever legal basis is being relied on for a given jurisdiction.