The primary coil is connected to an alternating current supply
which sets up a changing magnetic field.
This changing magnetic field is linked to
the secondary coil by the soft iron core.
The changing magnetic field "cuts" the secondary coil,
inducing an alternatin emf.

The transformer is based on Faraday's Law of Induction

Faraday's Law of Induction	Transformer
magnetic field	the soft iron core acts as an electromagnet with the primary coil
wire (conductor)	secondary coil
movement (coductor cutting across magnetic field)	alternating current supply in the primary coil causes a changing magnetic field

The transformer cannot with a direct current supply since the magnetic field will be steady. When there is no change in magnetic field, there is no "movement", there will be no induced emf.