Client-side prediction
The client applies your input immediately and guesses the outcome, instead of waiting a round trip for the server to confirm it.
In an authoritative networked game the server owns the truth, but waiting 50–150 ms for it to acknowledge every keypress would make the controls feel like mud. Client-side prediction runs the same simulation locally and moves your character the instant you press a key, then reconciles when the server's authoritative state arrives — if they disagree, the client rewinds and replays its unacknowledged inputs from the corrected state.
The technique was spelled out in the writeups around Quake III and Half-Life's networking (late 1990s to 2001) and is now standard. Remote players are smoothed with interpolation or dead reckoning instead, since you have no inputs to predict on their behalf.