Programs wrote temporary information to tape, keeping a room full of drives whirring constantly. There was no security to speak of. Eventually the university wised up and bought an additional Univac with no student accounts or dial-in lines, which ran all of the grading and billing software. It wasn't till the very late 60s that even the smallest MOS memory chips became available. Four wires run through the center of each core, four wires tediously strung, by hand, by Asian women who no doubt worked for a pittance.
Cores are tiny magnets, each remembering just one bit of information.
As we know from basic electromagnetics, a changing voltage creates a magnetic field, just as a change in a magnetic field induces a voltage. The wires running inside of the ferrite beads create the fields that flip the direction of magnetization, writing a zero or a one. They also sense the magnetic field so the computer can read the stored data. Two of the wires organize the core into an X-Y matrix. The core plane is an array of vertical and horizontal wires with a bead at each intersecting node.