No wonder Samael wants this thing, its COURSING with power! — The Watcher, right after War rips the heart from Tiamat.
The Hearts of the Chosen are very powerful items that are gained by killing Tiamat, The Griever, Stygian and finally Silitha. Samael requests these items to open the way to the Destroyer's Tower as he tells you. Over the course of the game it is revealed that Samael was not completely truthful about the nature of the Chosen; they never guarded the tower and their existence was dedicated to dividing Samael's power and keeping him from rising. Once all the hearts are back in Samaels possession his body begins to overflow with incredible power. He declares that he has regained his former full power, and is like unto a god with enough power to "suck the marrow from [War's] bones before he [War] drew another breath". Once they are all collected he allows entry to The Black Throne via portal.
Given the true nature of the Hearts of the Chosen they are very desirable. Vulgrim shows an extreme passion for these after War first acquires it. He allows the use of Serpent Holes to travel throughout The Destroyed City only after looking upon the heart of Tiamat. The Watcher also senses the power in the heart of Tiamat, saying that it was "coursing with power".