In English when we have: a singular definite article ("the"), a plural definite article (which also happens to be "the"), a singular indefinite article ("a" or "an") but no plural indefinite article.
In French there are also: singular definite articles (le, la, l'), a plural definite article (les), singular indefinite articles (un, une), but they do have a plural indefinite article (des).
That is what is happening here. The sentence in English is We possess black bears (plural indefinite). So no article in English. But French does need one "Nous possédons des ours noirs".
Of course it gets a tad more complicated. If there is an adjective in between the des an the noun, then the "des" turns into a "de".
So if you were to say "We possess tall bears" it would be "Nous possédons de grand ours".