A Horror is a shadow of yourself that can be summoned by RNG, sleep, a Rune of Fear, or even certain messages on the walls. These will follow whatever creature they are cast upon, often you, and drain their health when nearby. These are either red or black, and spew particles of the same color.
When a Horror is summoned for you, the log will print the message "He comes..." This horror will be black and have a moderate lifespan. When a horror is summoned for a different monster, the log will read "Your fury takes form..." The horror that appears will be red and have a shorter lifespan.