First of all, free charges are those charges which are mobile and can move freely and charges which are not free cannot move freely.
Polarization in physics refer to the process of "POLEarizing", i.e., developing two centers of opposite charges in an object that attract the opposite charges similar to the poles in magnets. Bodies which have free charges can only be polarized. In most of the substances this free charge is the free electron's negative charge. These electrons are distributed uniformly throughout the body of a neutral object. When this body comes under the influence of an external electric field of the opposite electric charge, the free electrons being mobile move within the object itself towards the source of the external opposite electric field and thus one side of the object has an excess of electrons and becomes negatively charged while the other side has a deficit of electrons and becomes positively charged. This process of making a body charged by polarizing it is known as charging by induction.
In conclusion, for a body to be charged by induction, electrons must have the ability to move from one region to another region in the object and for this free electrons are necessary.We charge a body by induction by polarizing it.