Transformers are made with two coils of wire near each other.  There are different designs, but the typical symbol for a transformer is:
They're made with TWO coils of  wire wrapped near each other...
    When a current runs through one coil, it produces a current in the other coil.  We can vary the number of turns in the coils to change the voltage and current in the second coil. NOTE: Transformers only work with alternating current.  There must be a changing current to make the first coil affect the other one.  Direct current would only produce one pulse in the other coil.

In my zapper, the wall transformer's first coil (called the "primary") sees alternating current at around 117V.  It reduces this to only 12V in the other coil (called the "secondary").

Transformers can be described with these two equations:

Voltage primary / Voltage secondary =  # turns primary / # turns secondary

Current primary * Voltage primary = Current secondary * Voltage secondary

TERMINOLOGY: