The clock above is referenced to a synchronised server rather than to your own device, and the reading underneath tells you how far apart the two are. That difference is your device's clock drift. The measurement takes several round-trip samples and keeps the fastest, halving the round trip to estimate the one-way delay — the same basic idea as the Network Time Protocol, at much coarser resolution.
What 'atomic clock' means here
No web page contains an atomic clock. The chain runs from caesium and optical standards at national laboratories, through International Atomic Time and UTC, out over NTP to ordinary servers, and finally to this page. Each link adds a little uncertainty, so treat the reading as good to a few tens of milliseconds rather than to the nanosecond. How the real clocks work is in how atomic clocks work.
Why a few milliseconds is a good result
An unsynchronised quartz clock can drift by a second or more per day. If this page says you are within a couple of hundred milliseconds, your operating system is syncing properly and there is nothing to fix. If it says several seconds, something is wrong — the sync check explains what.