A transformer is an electromagnetic device that uses the principle of induction to enable an AC waveform to produce a varying magnetic field (flux) and couple energy through to another conductor, often referred to as a winding or coil. Transformers have a magnetically permeable core material through which the magnetic field is changing, and this change links the primary and secondary coils.

Transformers are used in applications where the signal needs to be changed from one impedance to another. They are also used when an AC voltage on the input needs to be de-referenced from its input impedances, typically referred to as a ground level. 

Different impedances on the two wires on the input relative to a ground cause a condition called unbalanced that makes the circuit subject to noise voltages relative to the ground reference. Transformer outputs have no fixed reference point (one may think of the middle point of the secondary coil windings as a floating reference point), and can therefore drive symmetric loads in a circuit that is balanced. Balanced in that it is symmetric with respect to impedance. Noise that couples on subsequent balanced lines can be encouraged to couple equally, called common mode noise.  Common mode noise is removed by sensing the differential voltage in the receiver.

Transformers are also used to change voltage and current ratios (step-up / step-down relates to the relative voltage change) based upon different numbers of coils on primary and secondary sides of the transformer. Many devices use transformers to step down the main AC power supply to a lower AC voltage, and then use diode rectification and a Filter to create a DC power supply.  A huge benefit to transformers is that the primary and secondary windings are electrically insulated from each other. This allows transformers to be used as isolating transformers,  having the characteristic of providing galvanic isolation. Galvanic isolation is the isolation of the grounds of the primary and secondary and thereby prevents current flow. This improves safety as it prevents shorts to ground that may be through a person’s body.