In FastAPI, path operation dependencies are functions that run before the main path operation function. When a request comes in, FastAPI first calls the dependency function to get needed values. Then it passes those values as arguments to the path operation function. For example, a dependency can extract query parameters or perform checks. This process helps keep code organized and reusable. The execution table shows the request flow: the dependency runs first, returns a value, then the path operation uses it and sends the response. Variables like 'q' start as None and get updated after the dependency runs. If the query parameter is missing, the dependency returns None, which the path operation can handle. This step-by-step flow ensures inputs are ready before the main logic runs.