The monster heart (a beating heart unidentified) is a reward given to you by <Mia> the cat freak. It cannot be used but simply having it in your inventory makes it easier to charm / dominate an animal and make it your pet. Having a monster heart will let you dominate monsters that are higher level than you.
The specific effect the item has on domination is to increase the domination spell's power by 50% The game only checks if a monster heart exists, not if multiple exist, meaning it does not stack.