A simple transformer consists of a laminated iron core, a primary coil and a secondary coil. An alternating current is supplied to the primary coil, producing a varying magneticflux in iron core.
The input voltage and the output voltage are related to the number of turns of the on the primary coil and secondary coil.
Turns on secondary coil / turns on primary coil = output voltage / input voltage
A step-up transformer has more turns on the secondary than on the first, and step-down has fewer turns on the secondary than on the primary.
For efficient transformers, the output power from the secondary coil is equal to the input power from it's primary coil.
In a step-up transformer, the voltage is stepped up but the current is stepped down. If the voltage is stepped up 100 times then the current is dropped 100 times.
Transformers can be made efficient by using low-resistance windings to reduce power losses due to the heating of the current. This can be possible with a laminated core with layers of iron seperated by insulator; minimises current induced by the core.
If the wire used to create the coils is thick enough, the resistance will be very small so most of the electrical energy supplied to the transformer will go into the load rather than being wasted as heat.
Another benefit of using iron in the core, is it's soft property which makes it very easy to magnetize and de-magnetize.
In the national grid, electrical power is transmitted at high voltages to minimize heat losses in the transmission cables.
The power loss during transmission of voltage is power = Current squared x Resistance = Orginal power x resistance / voltage squared .
The higher the transmission voltage, the smaller are the power losses through heating.