This is a core memory card for a Burroughs E2000 Electronic Accounting Desk Calculator from around 1964. The E2000 was not a general purpose computer, but a specialized electronic accounting machine. Thus the core memory was not for storing programs or applications, but small amounts of data for processing. This particular core memory card could hold about 100 alphanumeric words at a time.
Core memory uses many small iron rings barely a millimeter wide that can be charged magnetically (positive and negative) to store data. Each white wire you can see in the diagram leads to a grid of core rings arranged in a 52x52 array.
Clara Hamlin's sign is located on the lower back of the board. It is suspected that she is the worker who assembled the board. Clara could be the woman in the newspaper who is holding the memory module.
A photo of the E2000 can be seen in this newspaper advertisement from 1964.