In this situation, the heat transfer process is convection. Inside the pot, the hottest water rises to the top, because it's less dense, and the colder water sinks to the bottom, because it's more dense.
In this situation, the heat transfer process is conduction. The chef touches the pot, and burns himself, because the process of conduction is caused by the heat from the stove, moving through the pot. When he touches extremely hot pot, he gets burned.
In this situation, the chef is placing his hand above the stove, and feeling the heat being radiated from the stove. This process is called, "radiation".
In the picture to the left, it represents the sun radiating heat down on Earth. The ground conducts the heat, which then heats the air. the warm air rises, while the cold air sinks. This process is called convection.