This is the 13948th most frequent Turkish word.
mağaranın
"Of the cave" or "the cave's."
In this sentence, 'mağaranın' is used in the genitive case to indicate 'of the cave' as it is defining a possession or characteristic (inside the cave).
Mağaranın içinde eski bir harita bulduk.
Inside the cave, we found an old map.
Here, 'mağaranın' is indicating possession ('of the cave') and modifies 'the entrance' for clarity in the sentence.
Mağaranın girişine bir tabela yerleştirdiler.
They placed a sign at the entrance of the cave.
This usage of 'mağaranın' again in genitive case indicates 'of the cave' and relates it to 'the history' mentioned in the context.