Our is usually classed as a possessive determiner (or possessive adjective): a word that indicates possession (telling you whom or what something or someone belongs to) by modifying the following noun (e.g., “our grandmother”).
It’s normally not considered a pronoun because it doesn’t stand alone in place of a noun. But it is closely related to the possessive pronoun ours, and some grammars class our and other possessive determiners as “weak possessive pronouns.”
However, it’s more useful to define our as a determiner, because this more accurately describes its role in a sentence.