Manuscripts are a type of collectible in this game. You read them for some extra story content. You can keep track of these pages by selecting "Collectibles" from the main menu and going to "Manuscript Pages". It will show you the 3 areas in the game which you can check. Collecting these will let you unlock guns in story mode and some things in arcade as well. While in the game you can press or via the start menu look at what collectibles you have obtained. You can replay chapters from the main menu to pick up the ones you have missed. If you do this, it's suggested to do it after completing the game so that you don't over write your checkpoints. The manuscripts will appear different depending on which Act you are in, so that is something to pay attention to if following a guide.
A complete guide can be found HERE.