Horrors are creatures/spirits that date back to The Fourth World and earlier. They are able to access our world when the mana levels are high enough. In the Earthdawn universe, they are said to come from the "dark corners of the netherworlds." This would seem to correspond to the deep metaplanes that have been discovered.
In the Shadowrun/Earthdawn universe, magic goes through cycles. As the magic level rises, it allows Horrors to cross from their distant, otherworldly dimension into the human's world. The Horrors come in an almost infinite variety -- from simple eating machines that devour all they encounter, to incredibly intelligent and cunning foes that feed off the negative emotions they inspire in their prey. Some horrors were so powerful, that during the Scourge they killed or drove insane several Passions and similar god-level entities.
Critters in the Sixth World that might be modern manifestations of early Horror-arrivals include wraiths, nomad spirits and shedim. Insect spirits had, at first, been believed to be another manifestation of the Horrors, but instead have been identified as a threat that merely heralds the arrival of the Horrors.