"Hestene og ænderne drikker vand."
Translation:The horses and the ducks are drinking water.
It's an umlaut. These exist in all living Germanic languages. (Apparently, Gothic may have been the only Germanic language that didn't have them...)
Umlauts have become relatively rare in English, but they have survived in some of the most common words: goose/geese, man/men, foot/feet, mouse/mice. And they don't just occur in plurals: fox/vixen, come/came, fall/fell.
You can think of it this way: An e (or i) in a suffix influences how an earlier vowel is pronounced. The resulting modified vowel may have a pronunciation that is otherwise rare in the language. In the beginning, people wrote this as ae, oe or ue, but later various shorter ways of indicating the changed vowel quality became established, such as a with an e on top, ä or æ. (Or just an e, as in English.)
When do we use “ene" and when do we use “erne" for plurals with definite article?
it depends on the irregularities in the indefinite plural, some words dont take the r, others might have an umlaut (a -> æ)