How does an induction cooker work?

The single line answer is Eddy current.

In induction cooker, there is no flame or any heating coil.

                             The main part of an induction cooker is copper wire placed under the cooking pot. AC current is passed through the coil to make fluctuating magnetic field. So the metallic pot will be under the influence of this magnetic field.

[Eddy current is formed in a metal when it is placed in a fluctuating magnetic field ]

                            So here eddy current will be induced in the pot and it will try to flow in circular path through the pot. The material of the pot will be of  high resistance. So  the current will cause increase in the temperature of  the pot.

                                Suppose if we are using aluminium pot, the resistance of the pot is less.So the eddy current will flow through the pot easily, so temperature of the pot will not increase .So it won't work.

                                   Suppose if you are placing a any non conductor of heat (Paper,wood....) ,so there is no direct contact between the surface of the cooker and the pot , But still the pot will get hot because the pot is still under the influence of the magnetic field