A transformer consists of two magnetically coupled coils. Alternating current in one (called the "primary") creates a changing magnetic field which induces a current in the second coil (the "secondary"). A core made of iron or ferrite generally connects the two coils, but higher frequency devices can work without a ferrous core.
Transformers have two primary functions: Voltage transformation and isolation:
Primary applications are for power and for signal isolation / impedance transformation.
An autotransformer is a transformer with a single coil with intermediate "taps" to effect the changed outgoing voltages. They do not provide isolation.
Transformer capacity is rated in kilovolt-amps (KVA): The volts x amps / 1000.