The name
The name means 'those who from heaven came to earth'.
The rendering comes from Zecharia Sitchin. Assyriologists read a-nun-na-ki as 'princely offspring of An' — heaven is a lineage here, not a departure point.
Where the translation comes from
Sitchin parsed the name as three separate words — anunna plus ki, 'earth' — to produce 'those who from heaven came to earth'. Sumerian does not work that way here. The final -k is the genitive marker of the phrase, and the writing a-nun-na-ke4 in other contexts makes the grammar explicit. The god An supplies the 'heaven' element only in the sense that his name is also the word for sky.
What the word does in the texts
Usage shifts by period and place. In Sumerian literature the Anunnaki are often the great gods collectively; in Inanna's Descent they are seven underworld judges; by the Enuma Elish they are ranked staff assigned to posts above and below. No text treats them as arrivals. There is no verb of travel attached to the name anywhere in the corpus.
Why the error is durable
The false etymology is memorable, fits in a sentence, and answers a question the real one doesn't: it explains where they came from. Correcting it requires a paragraph about Sumerian case endings, which loses every argument it enters. That asymmetry, more than any evidence, is what keeps the claim in circulation.