Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
As the AI bot suggested, the PIN is device-specific; it is used to confirm your account on your PC.
Which type of subscription do you have? To share with your wife, you would want a Microsoft 365 Family (or 365 Premium) subscription, so that you can invite her to install Office with her own account. By using one and the same account, you are also sharing the file storage in OneDrive, which isn't necessarily what you want.