This is the 12222nd most frequent Turkish word.
haberlerine
"Haberlerine" means "to their news" or "about their news" in English.
Here, 'haberlerine' means 'your news' and is used to refer to specific news items associated with the second person singular.
Gazetede çıkan haberlerine çok sevindim.
I was very glad about the news appearing in the newspaper about you.
In this sentence, 'haberlerine' refers to the third person singular's news ('to their news') and expresses possession combined with the locative case.
Arkadaşının haberlerine güvenemezsin çünkü çok abartılı.
You can't trust your friend's news because they are too exaggerated.
Here, 'haberlerine' refers to news associated with television, using 'haberler' (plural of 'haber', meaning news) with the locative case.