The FileSensor task in Airflow starts by checking if a specified file exists. If the file is not found, it waits for a set poke_interval before checking again. This repeats until the file appears or the timeout is reached. In the example, the sensor checks every 5 seconds and finds the file at 10 seconds, then completes successfully. Variables like file_exists and task_state update accordingly. If the file never arrives, the task fails after timeout. This sensor helps workflows wait for necessary files before proceeding.