In FastAPI, you define a function and decorate it with @app.get or @app.post to register it as a route handler. The decorator tells FastAPI which URL path and HTTP method the function should respond to. When the server runs and receives a request, it checks if the path and method match any registered routes. If yes, it calls the decorated function and sends back its return value as the response. This example shows a GET route at '/hello' that returns a JSON greeting. The function is async to allow efficient handling of requests. The execution table traces defining the function, applying the decorator, receiving a request, calling the function, and sending the response. Variables like the function object, app routes, request, and response change state during these steps. Common confusions include why decorators are needed, what happens on unmatched paths, and why async is used. The visual quiz tests understanding of route registration, function calling, and HTTP method effects.