The SpiceDB HTTP API is an open-source feature that provides a reverse proxy to respond to HTTP requests, built using grpc-gateway. It allows users to explore SpiceDB and its API by making API calls through the HTTP API server, which can be run locally on the user's machine. The API uses a preshared secret for authorization, and users can browse available operations and models, including an OpenAPI spec generated alongside the API proxy. Users can also make API calls using tools like curl or Postman, with example requests provided to help them get started.