Your Grimoire contains cards that you can view on bungie.net or the app. Each card gives background lore on guardian classes, characters, enemies and locations you've encountered, etc. If you open a particular card there's a description tab for lore and a progress tab for rank in kills and providing your character's k/d ratio, location completions, etc. In the progress tab there are also in game bonuses revealed for your completion of Grimoire objectives.