Interpolation predicts past states for objects controlled by other players based on the current state and previously known states. For example, the position of a vehicle can be interpolated to be in-between a past known location and its current known location.
The below figure depicts an example of interpolation. At the left at time t0, the client displays the known state of the game world at that time. At the right at time t2, the client has gotten an update on the world state. At time t1 in the middle, the client interpolates the position of the green avatar based on the known position in the past at t0 and the known position in the future at t2. The client then renders this predicted state. Interpolation is typically used to visually smooth out game states rendered on the client in cases where the visual update rate happens more often than do updates received from the server.
Paul Sharkey, Matthew Ryan and David Roberts, 1998. A Local Perception Filter for Distributed Virtual Environments
Jouni Smed, Henrik Niinisalo and Harri Hakonen, 2004. Realizing Bullet Time Effect Multiplayer Games with Local Perception Filter
Cheryl Savery, T.C. Nicholas Graham, 2013. Timelines: Simplifying the Programming of Lag Compensation for the Next Generation of Networked Games
Cheryl Savery, T.C. Nicholas Graham, 2014. Reducing the Negative Effects of Inconsistencies in Networked Games
Wai-Kiu Lee and Rocky Chang, 2015. Evaluation of Lag-Related Configurations in First-Person Shooter Games
Yahn Bernier, 2001. Latency Compensating Methods in Client/Server In-game Protocol Design and Optimization
Glenn Fiedler, 2015. Physics for Game Programmers : Networking for Physics Programmers
Benjamin Goyette, 2016. Fighting Latency on Call of Duty: Black Ops III
Tim Ford and Philip Orwig, 2016. Developer Update - Let's Talk Netcode
Matt Delbosc, 2017. Replicating Chaos: Vehicle Replication in Watch Dogs 2
Peter Andreasen, 2018. Deep Dive into Networking for Unity's FPS Sample Game
Shengmei Liu, Xiaokun Xu and Mark Claypool. A Survey and Taxonomy of Latency Compensation Techniques for Network Computer Games, ACM Computing Surveys, Article 243, Volume 54, Issue 11S, DOI https://doi.org/10.1145/3519023, September 9, 2022. Online at: http://www.cs.wpi.edu/~claypool/papers/lag-taxonomy/