This is the 14252nd most frequent Russian word.
оставляя
"Leaving" or "letting remain."
The word 'оставляя' is used in this sentence to indicate an action or state concurrent with the subject 'он' leaving, as it illustrates what happens at the same time.
Он ушёл, оставляя нам свои вещи.
He left, leaving us his belongings.
Here, 'оставляя' exemplifies the result or effect of the teacher's speaking on the listeners, expressing a consequential state.
Учитель говорил, оставляя нас в размышлениях.
The teacher spoke, leaving us in thought.
In this sentence, 'оставляя' describes a simultaneous ongoing action that complements the subject's main activity of playing.