This is the 311th most frequent Czech word.
naší
"Naší" is the dative or locative form of "our" in Czech.
In this sentence, 'naší' is the genitive form of the possessive pronoun 'naše', matching the feminine singular noun 'rodiny' to indicate possession (our family's photo).
Toto je fotografie naší rodiny.
This is a photo of our family.
Here, 'naší' is the dative form of the same possessive pronoun, used with the feminine singular noun 'restaurace' to indicate relation or motion (to our restaurant).
Šli jsme do naší oblíbené restaurace.
We went to our favorite restaurant.
In this example, 'naší' is in the instrumental case, agreeing with the feminine singular noun 'učitelkou', and indicates the entity the action is related to (with our teacher).