This is the 13626th most frequent Turkish word.
kurtarıldığını
"That (something) was saved/rescued."
In this sentence, 'kurtarıldığını' is used as the object complement of the verb 'öğrendik' (we learned). It conveys that the information being learned pertains to the fact that there was an act of rescuing being performed on the animal.
Hayvanın, derin çukurdan kurtarıldığını öğrendik.
We learned that the animal was rescued from the deep pit.
Here, 'kurtarıldığını' functions as the object clause to the verb 'söyledi' (he/she said). It implies the statement made includes that an act of rescue happened instantly.
Onun, tehlikeden anında kurtarıldığını söyledi.
He said that she was immediately rescued from danger.
In this usage, 'kurtarıldığını' serves as the complement of the verb 'anlayabiliyoruz' (we can understand). It expresses the conclusion or realization regarding an act of rescue happening.