Transformer works on the principle of mutual inductance.
Inductance is the property where the coil opposes the change in current.
In mutual induction, the coil opposes the change in current by developing an induced emf.
The simplified image of the transformer is shown below
Here, the v_i represents the input voltage and v_o represents the output voltage.
The input voltage is connected with coil A which is wounded on an iron core.
The current flows through coil A, this current, in turn, generates a magnetic field around it.
This magnetic field produces the current in coil B, the voltage output is obtained across the v_o.
Eddy current can be reduced by using thin laminated sheets separated by insulated sheets.