It renders your title and description the way Google's desktop results page does — same font, same sizes, same blue-link and grey-text treatment — and measures their rendered width in your browser to decide exactly where Google would cut them off and insert an ellipsis. Nothing you type is sent anywhere; the measurement happens entirely on your machine.
To check what a page is currently serving rather than what you plan to write, run it through the Meta Tag Analyzer, then paste the values here to iterate on them.