A head is the reading/writing device used to store data on a magnetic medium in devices such as a drum, disk or magnetic tape. They are identical in basic concept to the head on a magnetic tape recorder, and were initially created to record audio on magnetic tapes and wires.
The head consists of a roughly toroidal piece of material which is very permeable to magnetic fields. This piece has a small slot cut out of it at one point, the 'gap', which is where the reading and writing happens; and a wire coiled around the body of the toroid.
For writing, when current flows through the wire, a circular magnetic field is created in the toroid; when the field gets to the gap, without the permeable material to contain it, it spreads out somewhat in passing from one face to the other.
The surface coated with magnetic material which is where the recording is to be made is brought up close to the gap, and moved past it; the magnetic field escaping at the gap magnetizes the magnetic coating in one direction or another, depending on the direction of the current through the coil.
For reading, the process is reversed; the recorded material is brought close to the gap, and moved past it; the magnetized regions of material on the surface create a very small field in the toroid, and thus very small currents in the coil, which can be amplified and detected.