'Us' is the accusative form of 'we'. I don't know if you have cases in Polish, but 'we' becomes 'us' if it's the object of a verb for the same reason 'I' becomes 'me' and 'they' becomes 'them'. Fortunately, English only has cases for pronouns (although it'd be better if we didn't have them at all!).
'Our' is the possessive adjective form of 'we'. As its name suggests, it's used before as an adjective before a noun to indicate possession. It's just like 'my', 'your', 'their' etc.
Ex.
Our house = The house that we own.
'Ours' is the possessive pronoun form of 'we'. It is used to indicate possession when you don't want to repeat a noun. It's just like 'mine', 'yours', 'theirs' etc.
Ex.
Our house = The house that we own = The house that is ours
"That car is yours, but this one is ours."