Have a look at this:
your | il tuo regno | i tuoi regni | la tua volontà | le tue volontà |
our | il nostro pane | i nostri pani | la nostra terra | le nostre terre |
You should recognise the nouns and articles from last time. What we have here is the form in which you'd usually find 'you' and 'our' added in. They're the only two possessive forms in the Padre Nostro - no 'my', 'his', 'her', 'its' or 'their' to worry about.
You can see that the forms "agree" with the nouns, that is the forms vary from masculine to feminine, and singular to plural, but it's not really so hard for the main part. On the other hand, this can get confusing for English speakers. Take the following, for example:
1. il suo nome
2. la sua volontà
1 can mean "his name" as well as "her name", depending on the context. 2 can mean "his will" and "her will", depending on the context. What it is tempting to do is think that 'suo' means 'his', and 'sua' means 'her', but both can mean either. It's the noun that it agrees with, not the person.
Again, 'volontà' hasn't changed in the plural, but from 'le tue' you can see it's feminine plural.
You probably noticed though, that the Padre Nostro doesn't start "Il nostro Padre", as you might expect from the table above. I don't suppose you'll lose any sleep over it, but I'll try and explain anyway. Relations are a special case; generally speaking you ditch the article (mamma mia!), except when it's in the plural (i nostri padri). I don't have a particular explanation for why 'nostro' is after 'Padre' here, but I don't intend to worry too much about it. Most adjectives, in fact, come after the noun in Italian, but let's burn that bridge when we come to it.
che
'che' basically means 'that' or 'which'. However, it also means 'who' as it does here. There is an Italian word for 'who', but it's out of place here, because this 'who' elaborates on who the Father is. In Italian therefore 'che.'