The word ci has three main meanings:
- The clitic version of the second person plural object pronoun (both direct and indirect). In this context it has a meaning roughly similar to the English us. For example
Il cane ci ha morso
(The dog bit us)
- The second person plural reflexive pronoun. Those pronouns mainly indicate that the verb is in the reflexive voice. In this guise it often plays the role of the English word ourselves or the word each other, for example:
Ci divertiamo
(We enjoy ourselves)
Ci baciamo
(We kiss each other)
Note that in English the reflexive voice is often expressed by the lack of pronouns or by adding the possesive adjective to the object. A full treatment of the reflexive voice in Italian deserves its own question, so if you're interested don't hesitate to ask!
- As an adverb. In this case it has the same meaning of the English word there.
Ci sono andato
I went there
The example you link to falls in the third usage, although as a fixed expression it might be a bit complicated for a beginner to figure it out. The meaning is as follows
Che ci vuoi fare
What do you want to do about it
In this case ci has a figurate meaning, so rather than a physical location it indicates the whole situation you are speaking about. This particular sentence is often used to indicate resignation in the speaker (as in, There's nothing we can do about this).
For further examples, please take a look at this answer.
PS Since in the question you indicate that you think that our is a translation of ci, I would like to point out that this is incorrect: the more correct perspective is that both ci and our can be markers of the reflexive voice. Even in those cases ci can never be replaced by our in the same position of the sentence.