Use our when a noun follows it: Our flight leaves at six. Use ours when the noun is already understood and nothing follows: Their garden is bigger, but ours gets more sun. There is no such word as "our's".
The core difference
Both words mark something as belonging to a group that includes the speaker. The difference is purely grammatical position. Our is a determiner — it sits in front of a noun and cannot survive without one. Ours is a possessive pronoun — it replaces the whole noun phrase.
Compare: our car (determiner + noun) and ours (the car we own, in one word).
How to use each
- Our + noun: Our neighbours have a new dog. / We sold our tickets. / It was our fault entirely.
- Ours alone: That table is ours. / Yours arrived on time; ours didn't. / The decision was ours to make.
One phrase to memorise: a friend of ours. Never "a friend of our" — the noun already appeared earlier in the phrase, so the pronoun form is required.
The test
Cover the word and look at what comes immediately after it. If a noun phrase follows — a noun, or one or more adjectives running up to a noun, as in our new car — write our. If nothing follows but a full stop, comma, or verb, write ours.
A second check works just as well: swap in my and mine. If my fits the slot, you want our; if mine fits, you want ours. This seat is mine → This seat is ours. My seat is here → Our seat is here.
The apostrophe trap
Because English forms most possessives with an apostrophe (the company's policy), people reach for one here too. Don't. Possessive pronouns — ours, yours, hers, theirs, its — are already possessive and never take an apostrophe. "Our's" and "their's" are always errors, in every register, in both British and American English.
The only apostrophe you will ever see near these is the contraction it's, which means it is and is a different word from the possessive its.
The edge case
Watch for coordinated possessives, where the noun is delayed: your problem and ours is correct, but your and our problem is clumsy though not ungrammatical — most writers rephrase to the problem we both have. And in headings or lists where the noun is implied, ours is the right choice: Theirs: 40%. Ours: 60%.