This is the 5330th most frequent Russian word.
оставив
"Having left" or "leaving behind."
Here, 'оставив' is a short participle form from the verb 'оставить', signifying an action completed by the subject preceding the main action described.
Оставив книгу на столе, он ушёл из комнаты.
Leaving the book on the table, he left the room.
In this sentence, 'оставив' describes the means by which the subject's main action was performed.
Она быстро передала послание, оставив его в руки друга.
She quickly delivered the message, leaving it in the friend's hands.
Here, 'оставив' indicates a concurrent action related to the main activity of the sentence.