Live time, redrawn on every animation frame rather than once a second, so the milliseconds actually move rather than stepping. The time comes from your device's own clock, which means this page is exactly as accurate as your computer is — and if your computer syncs to a time server, that is accurate to a few milliseconds.
Where the time actually comes from
A web page has no clock of its own. It reads the operating system's clock, which is kept in step by the Network Time Protocol against far more accurate reference clocks upstream. So "live" here means "as live as your machine" — covered in how accurate is a browser clock and NTP vs browser time.
Why milliseconds need animation frames
A timer set to fire every 250 ms drifts, and browsers throttle timers hard in background tabs. Redrawing on the display's own refresh cycle keeps the readout smooth and honest. The mechanics are in millisecond precision in the browser.