Monster Information is gained as you kill monsters.
This Info lets you receive just 90% damage from the monster, where as you will deal 110% damage to them.
Having this Info lets you see, where the monster is appearing in the world. In addition, you can auto-move to them.
With this info, you will get twice as many item drops from the monster.
When you have Origin Information on a monster, you will receive an additional 10% Experience from that monster.
Origin Info show up in your list of sharable infos yellow. Only 2 Origin Infos per day can be received on each player character. Receiving these gives you bonus Experience as part of your daily Diary bonuses.
You can share Monster Origin information an unlimited amount of times per day. Sometimes you'll get all 4 stages fast, other times not so fast. Good thing is you can have someone teach you the parts, if they know them and of course receive information from other players.
Press Alt+M to see all of your collected Monster Information.