LitRPG is a genre of literature in which the main protagonist, and often all characters, live in a game-like system. They generally have direct access to D&D or video game style stat sheets, on which, through meditation, focus of will, or a HUD system, they can see their level, hit points, mana, xp, abilities, etc.
This can work out surprisingly well. It gives an additional motivation for events in the story, gives immediate feedback on the importance of encounters, gives a clear indicator of growth, and intertwines two narratives -- one of fighting monsters and one of leveling.
LitRPG covers a wide range of styles: in some stories, the characters are very much in computer game mode, where their lives are built around dungeon crawling to gain levels; in others the gamification of their lives is incidental, just a different type of magic system, but not their primary motivation; often it's a combination, where at times the plot might require grinding to level up or gain a new stat, but that's just one event in a grander story.
This genre is a fairly direct descended of on-line fanfic. As with any genre, some readers will enjoy it more for the tropes common to the genre, and some more for the quality of writing. However, any good LitRPG makes exploring the RPG system an interesting part of the story. This often involves munchkining and discovering new powers, and LitRPG has some overlap with superhero fiction and progression fantasy, while the settings involved often place them squarely in the science fiction and/or fantasy genre. That said, LitRPG is limited only by the author's imagination, and might include any style of writing or type of narrative.