So, Grimoire isn't totally fleshed out in the Alpha, but they are basically the Commendations from Reach. Whenever you get so many kills/headshots/melee kills/etc., you unlock a Grimoire card which is applied to your profile. You can also earn Grimoire cards by finding these things called Dead Ghosts while in Free Roam in Old Russia. I loved hunting for those. I would enter old buildings and see a glowing Ghost sitting on a table. Once you revive it, it transports away, and you are rewarded a Grimoire card for it. The Grmoire cards also provide some cool lore for the game when you look them up on the site. That feature isn't available yet though. :)