(http://img.timeinc.net/time/photoessays/2007/vintage_computers/vintage_computers_10.jpg)
Cores are rings of ferrite suspended in a grid of wires (visible in the right third of this frame). A charge to a point on the grid magnetizes the ring in a clockwise or counter-clockwise direction, which corresponds to a one or a zero: one bit. Because it holds its state, core memory is able to retain information even when the electricity is turned off, thereby paving the way to modern computing.
These were hand-woven, by the way. Can you imagine weaving each bit of your computer memory by hand? :)