CNAME record
A DNS record that points one hostname at another, which is how a custom domain is attached to a shortener.
It says "go.example.com is an alias for whatever this other name resolves to", so the shortener can change its own infrastructure without every customer editing DNS.
A CNAME cannot sit at the root of a domain in standard DNS, which is why shorteners ask for a subdomain. Some providers offer a flattening record that works around it.
Propagation is usually minutes rather than the 48 hours folklore suggests, and it is bounded by the TTL of the record you replaced.