The Demon's Souls servers are officially shut down as of February 2018. For a temporary workaround to access accurate IGTIn-Game Time, please see this Reddit thread!
In-game time (or IGTIn-Game Time) refers to the time a game keeps track of internally. This may or may not include load times, time spent in cutscenes, and doesn't include time the game is not running (obviously) and times when a previous save file is loaded, from which where the timer resumes. It is usually displayed at the load savegame screen, in the pause menu or in a statistics menu during the game.