Interpolation delay
Interpolation delay draws other players and creatures slightly in the past, between two received positions, so they move smoothly on an uneven connection.
Also called entity interpolation, interpolation buffer, jitter buffer.
Messages over the internet arrive unevenly. If other players were drawn at the newest position received, they would jerk forward whenever a late message arrived. Drawing them a moment in the past, between two positions you already have, keeps them smooth, at the cost of showing them slightly late.
How long should the delay be?
It's a trade. Too short, and on a shaky connection the next position hasn't arrived when it's needed, so things freeze or jump. Too long, and everything you see is old, which makes attacks harder to dodge. A fixed delay is wrong for most connections, so the best delay follows the connection.
Interpolation delay in Mytheria
The game measures how much buffer each position message would have needed, and keeps the delay at the 95th percentile of the last 8 seconds plus 12 milliseconds, between 50 and 200 milliseconds. When the buffer needs to grow, the drawing clock runs up to 20 percent slower until it has, and up to 5 percent faster while it shrinks, so nothing jumps backwards. If messages stop for a moment, things keep moving the way they were going for up to 150 milliseconds before they stop and wait.
The full post, with clips and demos How to hide lag in an online co-op game