This is the 13914th most frequent Russian word.
обосновался
"Settled" or "established oneself."
Here, "обосновался" is used to indicate that someone has established themselves or made a settlement in a new location.
Он обосновался в новом городе и начал работать.
He settled in a new city and started working.
In this usage, "обосновался" reflects taking residence in a place specifically for a purpose.
Писатель обосновался в горной хижине для работы над книгой.
The writer settled in a mountain cabin to work on his book.
Here, "обосновалась" is used figuratively to describe the company firmly establishing its presence in a particular domain.