A daemon is a program that runs in the background usually without direct
user interaction. In the windows world this is called a service.
A headless system is a computer system or device that has been configured to operate without a monitor (the missing "head"), keyboard and mouse (KVM). A headless system is typically controlled via a network connection, although some headless system devices require a connection to be made via RS232 for administration of the device.
A headless programs is one that can run on such a machine.
So joined together a headless daemon is a process running in the background not requiring any KVM resources.