The Anunnaki are a group of Sumerian mythological deities. The name "Anunnaki" means something to the effect of 'those of royal blood' or 'princely offspring'.
There is a popular New Age belief that the Babylonian Anunnaki were extraterrestrial god-men that arrived on the earth to create a species of slaves (mankind), from recombinant genetics and apes, to work gold mines for them and be their servants. This popular myth was largely encouraged by the works of one Zecharia Sitchin in his book, The Twelfth Planet. The Anunnaki were supposed to have come to the earth from a planet called "Nibiru", the supposed "twelfth planet" in the solar system. The Anunnaki figure in much Babylonian lore.
Ancient Sumer-Babylon, like many cultures of antiquity, produced mythologies to explain the world around them. The Epic of Gilgamesh is one such mythology. Several versions of the epic poem exist, but the 12-tablet Akkadian version is the best known. The story centers on the friendship between the principal character, Gilgamesh, and Enkidu. Gilgamesh, the king of Uruk, is two-thirds god and one-third man. He has oppressed the people of Uruk, so the gods create Enkidu to distract Gilgamesh. Their unlikely friendship results in a journey of fantastical adventures resulting in the death of Enkidu.
An important feature of this epic is a “flood” story in which a character named Utnapishtim and his wife survive a great flood and obtain immortality. The existence of this flood story, with its many similarities to the Genesis account, indicates a common source. Rather than the Genesis flood account being copied from the Epic of Gilgamesh, both accounts are entirely separate records of something that actually occurred, namely, a global flood. The gods who appear in the Epic of Gilgamesh are the Anunnaki, a name that probably means “those of royal blood” or “princely offspring” in the ancient Sumerian language. In contrast to this pagan mythology is the biblical account of the Nephilim. Who were the Nephilim? Biblically speaking, the Nephilim were the descendants of the sons of God and daughters of men Genesis 6:1-4 . While there are differing interpretations of this passage, GotQuestions.org believes it involves the fallen angels (sons of God) taking on human form and mating with the daughters of men (human females), thereby producing a race of angelic-human half-breeds.
Is there a connection between the Anunnaki and the Nephilim? Perhaps. It is definitely interesting to note that both the biblical flood account and the Epic of Gilgamesh mention supernatural, god-like beings interacting with humanity in connection with a global flood. So, it is possible that the myths regarding the Anunnaki originate in the reality that was the Nephilim.