The term Anunnaki (alternate spellings: Anunnaku, Anunna, Anuna) is applied inconsistently, and the meaning appears to shift over time. It may be a term applied to a pantheon of the gods of the heavens and the underworld, or the term may be used to refer to the underworld gods only, or it may refer specifically to seven underworld judges, among others.
The common thread seems to be that they are a group of gods, and they decide the fates of men.
In Enki and the World Order they are stated to be a set of gods who decide the fates. Enki is clearly identified as an Anuna god here as well (not quoted).
The Anuna, the great gods, have taken up dwellings in your midst, and consume their food in your giguna shrines with their single trees. Household Sumer, may your sheepfolds be built and your cattle multiply, may your giguna touch the skies. May your good temples reach up to heaven. May the Anuna determine the destinies in your midst."
In the Enuma Elish (tablet VI), Marduk divides the Anunna into 300 assigned to the heavens, and 300 to the netherworld:
King Marduk divided the gods,
All the Anunnaki into upper and lower groups.
He assigned 300 in the heavens to guard the decrees of Anu
And appointed them as a guard.
Next he arranged the organization of the netherworld.
In heaven and netherworld he stationed 600 gods.
In Erra and Ishum, the Anunna appear in a similar fashion, but are now specifically the set of underworld deities, while the term Igigi is applied to the gods of the heavens.
For that time I will govern and keep strong the regulation of heaven and earth,
I will go up to heaven and issue instructions to the Igigi gods,
I will go down to the depths and keep the Anunna gods in order.
In the Descent of Inanna they are identified specifically as the seven judges of the underworld.
Then she made her sister Erec-ki-gala rise from her throne, and instead she sat on her throne. The Anuna, the seven judges, rendered their decision against her. They looked at her -- it was the look of death.
And similarly, they also appear specifically as judges of the underworld in the Epic of Gilgamesh (page 18)
When the Anunnaki, the judges, come together, and Mammetun the mother of
destinies, together they decree the fates of men. Life and death they allot but the day of death they do not disclose
The article "Anunna (Anunnaku, Anunnaki) (a group of gods)" by Nicole Brisch provides some further details on the varying meaning of the term.