How can you have heat without fire?
It's not magic, it's science. Specifically, the science of induction, where strong electric fields can create heat. Induction cooktops use this to heat food without any flames or direct heat, cooking more efficiently than their gas or conventional electric cousins. And this lack of direct heat makes them safer, too: you can even put paper between an induction cooktop and a pan, and it won't catch light.
Induction cooktops are also more efficient than other types of cooking methods. Because the heat is generated inside the base of the pan, they use less electricity than conventional electric cooktops, and can heat things quicker. They are also easier to clean, because the flat glass or ceramic surface has no gaps or grills to collect spilled food, and the food doesn't get burned onto the surface. If you spill something, one quick swipe with a damp cloth will clean it up. They are also quicker to control and more precise, again because the heat is generated inside the cookware, and so react quicker when you turn the dial up or down.
So why aren't they more common? It's partly a comfort thing; most US consumers don't like them because they grew up on gas rings. Cuhe has recently introduced an interesting solution to this problem: a cooktop that projects an LED flame that shows the ring is on, and indicates the heating level.
By the way, because of the way they work, many types of pans just don't heat up with induction cooktops. If you have copper bottom, glass or aluminum pans, they don't get hot when you put them on an induction cooktop.
How they work
Induction cooktops use one of the odd quirks of electromagnetism: if you put certain materials into a rapidly alternating magnetic field, the material absorbs the energy and heats up. That's because the field creates electrical currents inside the material, and the resistance of the material converts this electrical energy into heat, which is transferred to the food inside the pan.
Right underneath the cooking area of an induction cooktop is a tight spiral of cables, usually made of copper. The cooktop controller pushes an alternating current through this coil, which changes direction usually 20 to 30 times a second. This current flow creates a magnetic field above the coil. As the current alternates back and forth, the magnetic field does the same. If you put a pan on the surface (so it is just above the coil), this magnetic field induces (hence the name) an electrical current in the metal base of the pan. As the magnetic field alternates, this current flows back and forth (which is why it is often called an eddy current, as it swirls around like an eddy in a river). The metal resists this flow, and, like an electric heater, creates heat, which is conducted into the food through the metal of the pan. If you want to gently heat the food, the cooktop pumps a lower current through the coil, so the cookware generates less heat, and the food warms slower.
This process is only works with pans made of certain materials that have specific properties. In order to be heated by the magnetic field, the cookware has to be made of a ferromagnetic material, such as stainless steel or iron.
Electrons have a property called spin, where they can behave like a tiny magnet pointing in a specific direction. The reasons for this are complex (it gets into the crazy world of quantum mathematics and the strange nature of sub-atomic particles), but the basic idea is that, depending on where they are surrounding the nucleus of an atom, electrons spin on one direction (called up) or the other, called down. Ferromagnetic materials have an unbalanced set of electrons, where there are more up-spin electrons than down ones in each atom, or vice versa. This means that the atoms that make up the material can behave like a tiny magnet, and can be influenced by magnetic fields. The larger crystal structure of the material also helps by keeping the atoms aligned so this effect is increased.
Non-ferrous materials like zinc and most non-metals have a balanced set of electrons, where every up-spin electron is matched to a down-spin one. So, they aren't affected by magnetic fields nearly as much as the ferrous ones: the magnetic field only creates very small eddy currents that aren't enough to heat things up.
This does mean that there is an easy way to check if your pans will work with an induction stovetop. If you touch them with a magnet and it sticks to the bottom of the pan, they can be used on an induction cooktop. If the magnet doesn't stick, they won't work with induction. Many pan manufacturers are also now introducing a special mark on the pan that shows they are suitable for use on an induction cooktop: the Induction Mark.