What effects can happen in a tv for playing video games in it

Depends on what type of TV you have.

There is a chance with some TVs (Mostly CRT and old style Projection) that while playing games with HUD(Heads Up Display), or other objects in which their position on the screen doesn't change, an effect called burn in can happen. In which the image is litterally burned into the screen from many hours of play. Which results in a ghost image being visble even when not playing the game and in some cases as the tv is turned off.

TVs that used LCD or Plasma are much less likely to have this happen.