An electromagnetic coil consists of one or more loops (or turns) of a electrically conducting material. It has two primary uses: Firstly, it can be used to induce an electric current, by changing the magnetic field in which it sits (one could, for example, move a magnet through the loops), and secondly, by sending a current through it, it creates a magnetic field and thus becomes an electromagnet.
It is possible to combine these two abilities to make a transformer. This is done by sending a current through one coil, thus making a magnetic field that the other coil will respond to, inducing a current.
Wohoo, my first nodeshell rescue :-)