Bestiary is a system in Technical Alpha of Diablo Immortal that allows you to collect knowledge about monsters as you kill them. When you kill any monster, there's a chance they drop Monster Essence.
Bringing 10 Monster Essences to the Horadric Altar will unlock a random entry in your Bestiary. This can be done 3 times a day for the full reward.
As you unlock more entries, your Bestiary levels up giving permanent bonuses to your attributes.
The image above shows you an overview of your Bestiary Benefits and Progression at the Horadric Altar. In the Alpha there are 13 Boss Monsters, 23 Rare Monsters and 26 Common Monster to unlock with different rewards.
It takes time for to decipher a new Bestiary entry.
You can get the same entry twice but still get rewards in Terms of Experience, Gold and Items just no more permanent bonuses to your attributes.
For a Boss entry you can get up to half a million experience points which is a great way to farm Paragon Levels while increasing your overall character power.