Snapshot interpolation
The client draws the world a fraction of a second in the past, interpolating between two server snapshots so motion stays smooth despite sparse update packets.
An authoritative server ships snapshots of the world maybe 20–30 times a second. Drawn as they arrive, everything would stutter. Instead the client buffers the packets and renders a little behind the latest — often 100 ms — so there are always two states to interpolate between. Other players move smoothly without the client guessing.
The cost is delay: what you see is already stale, which forces shooters to pair the technique with server-side lag compensation. Valve's Source engine (2004) documented the scheme in detail and made it the default for networked FPS games.