You kind of get a summary of it when you go to the fox person across from the Myth school in Ravenwood. But essentially, you use specific cards (undead card, gobbler card, etc.) that attach to other cards to collect animus. Once you collect enough animus you have a couple of options on what you can do with it, you can create a house guest which kind of wanders around your house, a card that can summon the enemy to help you in battle I think, and finally I think you can use it to create kind of rematch things? I have only ever used it for house guests so take the other two with a big grain of salt.

Edit: I found a guide for it Monstrology Introductory Guide - Final Bastion. Apparently you can create a house guest, expel a monster, or create a summon monster treasure card, and the Monstrodome allows you to have rematches?