The Ancient Ones are a race of beings that lived on Earth long before mankind. They sleep under the earth and require blood from ritual sacrifices to stay sleeping for at least another year. In the case the ritual fails, they will wake up and destroy humanity. This is the case at the end of the film.
The ritual has been performed in one way or the other since the beginning of human history, being itself a primitive form of worship towards the Ancient Ones. Hadley rants that an undisclosed time ago, the Ritual was as simple as throwing a girl in a volcano but as time went on, the desire for entertainment grew within the Ancient Ones and so they demanded more complex rituals. The modern ritual constitutes an hours or days-long ordeal with multiple victims. Though allowing humans wide autonomy in the performance of the ritual, the Ancient Ones still imposed a few basic rules.
At some point within the modern times, The Organization assembled due the need for an organized effort to ensure a successful ritual to keep the Ancient Ones satisfied, including setting up facilities to perform several attempts around the world simultaneously, probably having a facility Director as the communication link between the Ancient Ones and mankind. Given the nature of the ritual, it is hinted that most global governments know about it on a top secret level, collaborating with resources and possible victims in a global conspiracy.
Every single monster is a manifestation of the Ancient One's desires for the punishment of human youth, and they are under the Ancient Ones' control. All the monsters were let loose during the System Purge, in which the workers at the Organization fell victim to the multiple monsters in the facility.
Marty Mikalski and Dana Polk escape the Purge and find the Ancient One's pit where they personally meet the Director who explains their situation. She tells Dana to shoot Marty, but Dana is attacked by the Werewolf, and the Director is attacked by Patience Buckner, who falls into the pit. Marty and Dana sit back and wait for the Ancient Ones to come, and one of them destroys the Facility and the Cabin.
Only seen briefly, they are shown to be gargantuan, one is seen to be lava-like and possibly a humanoid type creature. They dwell deep within the Earth's surface and largely powerful, despite being dormant, they are the source of power that ultimately controls (and possible creates) all of the monsters in every single facility around the world.
It is hinted that while they are not omnipresent nor omniscient, they can oversee a large context of simultaneous events around the world, as well as being ready to destroy mankind with little effort at any time. The full extent of their powers is unknown.
They are indicated to be sadistic, and cruel, forcing humans to sacrifice others in order to satisfy them. Initially, the sacrifices could've been very simple, but they have since become much more bloodthirsty, desiring for humans to not only die, but to die in violent, painful fashions, suffering in the process.
The main iconic concept is a clear homage/parody on the Cthulhu Mythos by revered author H. P. Lovecraft, as their might and true power is only hinted at, anger and source of peril towards humans but never depicted in detail, being more of a manifestation of abstract concepts such as primal fear to the unknown and the unbound hand that destroys the world.
However, they could be a modern take on greek titans and similar old mythological chaos creatures that tormented early humankind in most cultural backgrounds. There is an overwhelming amount of references to older gods in ancient religions including not only the Greek, but the Roman, Mesopotamian, Babylonian, Sumerian, Minoa and Vedic religions. Even in monotheistic religions such as ancient judaism and christian lore, there are similar ancient antagonists, such as Nephilim, Satan, Behemoth, Leviathan, and the symbolic creatures mentioned by Biblical authors such as Daniel and Jesus's apostle John in the Book of Revelation.
In the metafiction meaning, the whole film is a criticism to horror film clichés and conventions, down to the point of having the American Ritual itself as a play on the final girl trope. Given this fact, the Ancient Ones are a postmodern way the film authors (Drew Goddard and Joss Whedon) have their say on how the horror film fans have grown old of primal fears in films, constantly asking for different and more elaborate experiences in horror fiction that has lead to, ironically, many more chiché filled films and a decadence on the genre. In other words, the Ancient Ones are the public itself that is watching the film.