The Heartless Emblem is usually on/wore by a Heartless or someone that controls them. The emblem is also sometimes seen on buildings that are associated with them.
Heartless are beings born from the darkness of someone's heart and have many shapes and forms. They can only be defeated by a Keyblade wielder. They were first unleashed by Master Xehanort for helping Ven become a vessel. Artificial Heartless were created by Xehanort at Radiant Garden. Once a Heartless and Nobody are destroyed, the original person gets resurrected.