Extrapolation predicts future states for objects controlled by other players assuming current behaviors continue. For example, the position of a vehicle can be extrapolated to a future location based on its last known position and kinematic state (velocity, acceleration, orientation, and angular velocity).
The below figure depicts an example of extrapolation. At the left at time t0, the client display renders the known state of the game world at that time. In the middle at time t1, the state of the world has been updated by the server and the client displays the green avatar's new position, moving to the right. At the right at time t2, the client has not (yet) gotten an update on the world state, but can extrapolate the position of the green avatar based on the last known position at time t1 and the avatar's velocity. The client then renders this predicted state.
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