At a very high level, a viewer goes to the website, the website fetches data from the API, and then if they watch a stream the website also fetches the stream from the video edge.
When a Streamer goes live, they hit the video infrastructure, API Calls are made, and then the stream is pushed to video edge, where the viewers can pick it up and watch the stream.
You can check out the video infrastructure flowchart for a more in-depth understanding.