Question

Why is the core of a transformer made of magnetic material of high permeability?

Answer 1

A magnetic core is a piece of magnetic material with a high magnetic permeability used to confine and guide magnetic fields. By using a core of high permeability we become able to produce very much field so very much $flux$ to the secondary coil and which lead in a good $coupling$ of coils thus the good $efficiency$ of $transfer$ the power from primary coil to secondary coil.

we know the field is proportional to $\mu$ which is called magnetic permeability of the $medium$.