The Sin Hearts are demonic artifacts in possession of the Lord of Sin, Azmodan. The Sin Hearts beat with vile power, and can be used to empower entire demonic hosts, increasing their effectiveness greatly.
When Azmodan launched his assault on Bastion's Keep, he dredged the Sin Hearts from the depths of his realm in Hell. Locked away deep within Arreat Crater - Azmodan's seat of power - the Sin Hearts lend their strength to the hordes battering away at the Keep's gates.
Two Sin Hearts have been sighted in Arreat Crater, those being:
It is currently unknown whether those are the only Sin Hearts in existence.
The Sin Hearts are objects and quest requirements for the quest Heart of Sin. The Heart of the Damned can be found within the Heart of the Damned (area), within the Tower of the Damned. The Heart of the Cursed can be found within the Heart of the Cursed (area), within the Tower of the Cursed.
Both objects need to be destroyed in order to complete the quest. Beware; the Hearts are guarded by a mini-boss. Cydaea.