I see that you're also learning German, so that will make explaining this easier.
Think of it as "von uns." In this sentence, "ons" is just like "uns," and "van" is just like "von." In Dutch, "van ons" is simply another way to say "ours." You can do this for pretty much every pronoun. For instance, "van jou" means "je/jouw" and "van mij" means "mijn."
EDIT: Constructions with van + pronoun aren't really another way to use possessive adjectives as I had said. Just as English has both "your" and "yours," Dutch has both "je/jouw" and "van jou." The former is used when you place the possessive immediately before the noun, while the latter is used when you place the possessive someplace after. Here are some examples:
Dat is je/jouw eten. = That is your food. versus Dat eten is van jou. = That food is yours.
Het is mijn hond. = It is my dog. versus De hond is van mij. = The dog is mine.
The Tips & Notes provide a whole table listing the various ways of showing possessions, and I recommend you look through it. ^_^
I mean the notes for the Possessives skill. It explains the alternate possessives, which that falls under. I think I know better how to explain it now. Onze would be used if it was proceded by a noun. That's how the typical possessives work. However, it doesn't - it goes after the noun. In that case, you use either independent possessives (in which case you would say "De lunch is de onze.") or the alternate possessives (in which case you would say, "De lunch is van ons.").
It's all explained under the tips & notes under the possessives skill. I hope I did a better job at explaining it this time. :)
I love Duolinguo and find it very motivating and great fun. But it is rather irritating as I am a native speaker of English and the system tells me I am wrong when I use idiomatic English which doesn't seem to fit into your system: I said "It is our lunch." but it tells me I am wrong :-(((
It isn't because you used idiomatic English that your answer was marked wrong. That answer was marked wrong because it translates to "Het is onze lunch" in Dutch, not "De lunch is van ons." You can't really translate stuff differently like that, because the contributors that work on the course would have to manually add a lot of sentences to cover all the possible translations if approximate translations were to be accepted as well.
Just try to stick to more exact translations and you'll be fine. ^_^