How a transformer works

When an alternating potential difference is applied across the primary coil, an alternating current will flow in the primary coil. 

This alternating current through primary coil, will cause a changing magnetic field through the soft iron core. 

The magnetic field lines will cut the secondary coil, inducing an alternating potential difference across the ends of the coil. 

If the secondary coil is part of a complete circuit, then an alternating current will flow.