In FastAPI, shared dependencies are functions that provide values or logic reused by multiple endpoints. When a request comes in, FastAPI first calls the dependency function to get its result. Then it passes this result as an argument to the endpoint function. This way, the endpoint can use shared data or logic without repeating code. The execution table shows the request flow: receiving the request, calling the dependency, returning its value, calling the endpoint with that value, and finally sending the response. Variables like 'value' hold the dependency's output and are tracked through the steps. Understanding this flow helps beginners see how FastAPI manages dependencies behind the scenes.