DKIM, DomainKeys Identified Mail, is the mechanism of RFC 6376 by which a sending server signs a message with a private key and the receiver verifies the signature against a public key the domain publishes in DNS. The signature covers chosen headers and the body, so a message that is altered in transit, or that merely claims a domain it was never signed by, fails verification.
What Spaw answers
The domain endpoint reports dkim_selectors: which of the common selector names publish a key under <selector>._domainkey.<domain>. An empty list means none of the common names answered, which is not the same as no DKIM at all — a domain may sign under a selector nobody else uses — and null means the lookups failed. The free DKIM checker reads the same list.
What it does not mean
A published key proves the domain can sign, not that a given message was signed or that the signature aligned with the visible sender. DMARC is the policy that ties DKIM and SPF to the address a person sees.