Ours:
* "This park is ours, we spent all summer cleaning it up." (Shows possession)
* "Their house is bigger than ours, but ours has a beautiful garden." (Compares possessions)
* "We'll be back in an hour, you can use our car." (Indicates something belonging to the speaker and others)
Theirs:
* "Those toys are theirs, not ours." (Indicates possession by someone else)
* "They brought their own food, we didn't need to bring any of theirs." (Shows something belonging to someone else)
* "I think this book is theirs, they were looking for it earlier." (Speculates about ownership)
Combining both:
* "We'll be happy to share ours if you need to borrow some of theirs." (Shows both possession and sharing)
Remember that "ours" is used for things belonging to the speaker and their group, while "theirs" is used for things belonging to someone else.