The term "Anunnaki" originated in Sumerian Mythology. Meaning "those who dwell up on high" it is often used as a synonym for the Nefilim. In his works, Zecharia Sitchin, makes the case that these are extraterrestrials. He also presents evidence for why he thinks they are the inhabitants of an extra planet, called Nibiru.
Alex Collier, too, uses the word as a synonym of the Nibiruans. He claims the Anunnaki came into existence as a new 'tribe,' hundreds of thousands of years ago, when a civilisation from Sirius B and one from the Orion system merged after the marriage of the queen of the Orion group to the king of the Sirian group.
Other authors, such as Dr. Joshua David Stone, use the word to refer to the Negative Sirians, who were co-responsible for the downfall of Atlantis. Considering that the Nibiruans are negatively oriented and from Sirian descent, the 'stretch' in the meaning of the word to (include) the Negative Sirians as Anunnaki is an understandable one.
In some literature, the meaning of the word is taken one step further. Authors like Barbara Hand Clow use the word for anybody, human or extraterrestrial, who serves the negative or Secret Government agenda. In this sense, it would be synonym of the "Illuminati."