A no-KYC crypto exchange, sometimes called an anonymous or private crypto exchange, lets you deposit, trade and withdraw without ID verification: no passport upload, no selfie, no proof of address. That matters to people who do not want another copy of their identity documents sitting in a database that can leak, and to people in countries where mainstream exchanges will not open an account at all.
The catch is that "no KYC" on a homepage is not the same as "no KYC" in the terms. Many exchanges reserve the right to freeze a withdrawal and ask for documents after an automated risk flag. This page lists exchanges by what their terms actually say, and grades each one twice: once for how little it asks about you, and once for how likely you are to get your money out.
Three kinds of service get called a non-KYC exchange. Order-book exchanges hold your coins while you trade, and usually cap withdrawals for unverified accounts. Peer-to-peer exchanges match you with another person and, at their best, never hold your funds at all. Instant swap services convert one coin to another with no account. All three are ranked on this page, because the right one depends on whether you are trading, buying with fiat, or converting.