This is the 228th most frequent Turkish word.
başına
"Başına" means "to/on/at/over his/her/its head" or "per" depending on the context.
In this context, 'başına' denotes the idea of something affecting 'someone', often implying a challenging or unfortunate occurrence.
Evden çıkarken başına bir şey gelmesinden korkuyor.
He is afraid that something might happen to him when leaving the house.
In this sentence, 'başına' refers to the physical location 'on the head'.
Her sabah işe gitmeden önce başına şapka takar.
Every morning, he puts on a hat on his head before going to work.
Here, 'başına' implies an occurrence or an event happening 'to someone'.