The coil is a simple device -- essentially a high-voltage transformer made up of two coils of wire. One coil of wire is called the primary coil. Wrapped around it is the secondary coil. The secondary coil normally has hundreds of times more turns of wire than the primary coil.
Current flows from the battery through the primary winding of the coil.
The primary coil's current can be suddenly disrupted by the breaker points, or by a solid-state device in an electronic ignition.
If you think the coil looks like an electromagnet, you're right -- but it is also an inductor. The key to the coil's operation is what happens when the circuit is suddenly broken by the points. The magnetic field of the primary coil collapses rapidly. The secondary coil is engulfed by a powerful and changing magnetic field. This field induces a current in the coils -- a very high-voltage current (up to 100,000 volts) because of the number of coils in the secondary winding. The secondary coil feeds this voltage to the distributor via a very well insulated, high-voltage wire.
Finally, an ignition system needs a distributor.