The system you are using. Interactions between your computer and another computer on the Internet are sometimes described using the terms "local" and "remote" systems. The local system is your computer and the remote system is the other computer.

A computer (system) operated directly by the user rather than connected at arm's length via a communications link. E.g. a personal computer as opposed to a "remote" computer. LOL

An institution's computer system that manages cataloging, acquisitions, circulation, serials and/or an online catalog. If elements of a local system are designed to interact, can be called an Integrated Local System (ILS).