Translation:We know little about our grandmothers and grandfathers.
You use the pronoun "svůj" when the personal pronoun matches possessive, meaning "the subject's own". In this sentence you have "we - our", so you use "svůj". Analogically if the pronouns were: "I - my; you sg. - your sg; he - his; she - her; it - its; we - our; you pl - your pl; they - their" you would use "svůj" as well. Just be careful with 3rd person, because in that case the possessive might not be referring to the subject.
He knows little about his grandma.
In this case, "his" can refer to his own grandma (you would use "svůj" - On ví málo o své babičce.), but it can also refer to another guy's grandma in which case you have to use "jeho" - On ví málo o jeho babičce.
Svůj very loosely corresponds to the English “own” and indicates the possession by the subject of the clause. This is the pronoun we would use to translate “I love my dog.” - Mám rád svého psa.
Same goes here. At the same time "našich" is also acceptable, though "svých" is better Czech.