What is this ?
The processing of a signal ether analog or digital from the input to the actual display panel takes some time. This can usually be longer when the signal is processed for various reasons.
This lag is not the panel response time you usually find advertised in milliseconds, that refers to the time the screen takes to change the pixels after the signal is already processed.
When using a video game, the signal usually doesn't need to be enhanced by such processes, and much less needs be delayed by them.
How to measure it ?
What to do if I want to decrease it ?
The easiest thing to do is to turn off all those pesky processing modes. Many TVs have a game mode which does this for the most part.