This is the 873rd most frequent Icelandic word.
þeirrar
"Þeirrar" is the genitive singular feminine form of "sú," meaning "of that" or "of her."
In this sentence, 'þeirrar' describes 'stóra fjölskyldan' (the large family) in the genitive singular case, indicating that the memories belong to this particular family.
Við ræddum minningar þeirrar stóru fjölskyldu.
We discussed the memories of that large family.
Here, 'þeirrar' is again in the genitive singular case, relating to 'hugmynd' (idea), and is used to show possession of the descriptions being referred to as belonging to the idea.
Lýsingar þeirrar hugmyndar voru spennandi.
The descriptions of that idea were exciting.
Here, 'þeirrar' is the genitive singular form of the demonstrative pronoun 'sá', used to indicate possession or association with 'kona' (woman). It changes to match the gender, number, and case of the noun it is describing.