It's not a formally defined spec or standard — it's a design philosophy Kelsey Hightower champions, borrowed from intent-based networking (Cisco, etc.) and applied to APIs and infrastructure.
Kubernetes is the canonical example — you declare desired state, the control loop reconciles reality to match it. You never say "start container on node X, then update the load balancer" — you say "I want 3 replicas of this."
Contrast with imperative APIs: "do this, then that, then handle this error case." Intent-based APIs absorb the operational complexity on the platform side.