Short answer
SPF is a TXT record that receiving mail servers can check to judge whether the sending server is authorized.
What SPF looks like
An SPF record starts with v=spf1 and contains mechanisms such as ip4, ip6, include, a and mx. It often ends with -all or ~all.
Common problems
Multiple SPF records on the same domain are wrong. Too many include lookups can also make SPF fail.
SPF is not enough alone
SPF does not protect the full email chain by itself. DKIM and DMARC are needed for stronger protection and policy.
Common questions
Is ~all or -all better?
-all is stricter. ~all is often used during transition or when not all senders are known.
Can I have multiple SPF records?
No, SPF should normally be one TXT record combining all senders.