Those of you who have studied physics must surely remember that there are two things namely a permanent magnet and a temporary magnet. In a temporary magnet, the magnetism is induced as a result of some force which aligns the magnetic particles along a specific axis. This force could be due to rubbing of another magnetic material or an electromagnetic field applied using a varying current.
I will go a bit deeper and you can take a look at the typical magnetization curve below which shows the graph of magnetizing force H against the flux density B. When a material is in purely non-magnetized state and a magnetizing force is applied, the flux density rises along the dotted line OAC. But now if the current is brought to zero, the flux does not reduce to zero but a residual flux remains and the current has to be extended into the negative region (opposite direction) to bring B to zero again.
click to enlarge
Hence a loop is formed of the overall process as can be seen from the diagram and this is known as the magnetization curve for the material or is also known as the hysteresis loop. Now this property may be undesirable in several situations but here you can intuitively imagine a great use for the same. Once the signal is applied to the magnetic tape via the recording head, the section of the tape gets magnetized in accordance with the signal which leaves a residual flux on the tape. This acts to store that signal on the tape which can be played back using the playback head.