Induction cooking does not provide direct heat to a container but uses a high-frequency electromagnetic field generated in the cooktop by special coils to create a circulating electric current in the metal of the cookware. This electric current heats the cookware up the same as a coil on an electric stove is heated by the passing of electricity through it, and that heat then cooks the food in the container. When the field stops or the container moves away, the heating ends.
Wood counter tops are not safe to put an induction stovetop in. Sub-Zero, the maker of Wolf brand induction stovetops, states in its installation manual that, "Flush mount installations are intended for granite, solid surface or stone countertop surfaces only. Contact with hot cookware may cause damage to countertop surfaces that are not resistant to high heat."
Induction stovetops looked radically different when they first came out, and they are growing even more apart from other stoves. The surface was completely flat and smooth as glass, with the burners marked only with circles embedded into the surface. There was no visible sign at the burner level such as a fire or a red coil to let anyone know the burner was on.
Some induction cooktops now come with no burners at all, but sense where you place the cookware and its size. You can change from a small teakettle to a large roaster pan without having to worry about if you have enough burner space to place it. Holding your hand over the coils that are on will not hurt at all because no heat is generated, as long as you are not wearing any magnetic metals on that hand.