Client-side prediction
Also said as Prediction, Input prediction, Local prediction
With a server in charge, your own character moves the moment you press, on the assumption the server will agree. The server's answer comes a whole trip later.
Without it, a server-authoritative game makes every press wait for a round trip, and it feels like steering through treacle. Hardly any fast online game ships without it.
Say it
“Predict movement and jumping on the client, so they never wait for the server. Do not predict hits, damage or deaths: wait for the server, and show a small effect in the meantime.”
Where you’ve seen it
QuakeWorld added it in December 1996, as part of a revamp of Quake's network code for playing over the internet.
Not to be confused with rollback
Prediction here covers your own actions, the ones you already know. Rollback also has to guess the other player's, which you cannot know.