What is the difference between Noster and Nostrum?
We say "pater noster" but "panem nostrum".
Latin is an inflected language. This means that relationships between words are indicated by their endings. When an adjective like "noster" (our) modifies a noun, its ending must agree in gender (masculine, feminine, or neuter), number (singular or plural), and case (nominative, genitive, dative, accusative, ablative) with the noun that it modifies.
In the Our Father, since "pater" is nominative masculine singular, the form of "our" modifying it has to be the same. Thus: "noster," which is the nominative masculine singular form of "noster" (our). Since "panem" is accusative masculine singular, the form of "our" modifying it has to be the same. Thus: "nostrum," which is the accusative masculine singular form of "noster" (our)."
English doesn't change the form of an adjectives according to the noun that it agrees with. However, it is something like the difference between "her bread" and "his bread," in which the form in English changes according to the gender of the modifier.