Ferromagnetic memories, often referred to as core memory, utilize ferromagnetic rings through which wires are threaded to store binary data. By passing current in different directions, the magnetic polarity of the rings can be altered, representing binary values of 0 and 1. This setup allows for the storage and computation of information, as the ferromagnetic material can retain its magnetic state for a period, preserving the stored data. The technology is significant for its ability to maintain data integrity without continuous power, making it a foundational concept in the development of memory storage systems.