Magnetic storage is the storage of information in thin layers of magnetic material - very fine particles of magnetic material mixed with a binder, which caused the coating to adhere to the underlying surface. The material was originally an iron oxide formulation, but many different substances have been used.
The process uses a magnetic head to write small areas which are magnetized in one direction or another (depending on the direction of the 'write current' through the coil in the head).
For most of the lifetime of magnetic storage, these areas have had their magnetization direction parallel to the surface of the magnetic material; this was the easiest magnetization direction to create heads for. Recent developments have been the creation of heads which can write magentized regions in a vertical direction; those can be smaller, thus increasing the information storage density.