This is the 14000th most frequent Russian word.
объяснив
"Having explained."
The word 'объяснив' denotes an instrumental action of explaining that led to the main action of starting the lesson.
Он начал урок, объяснив новую тему.
He started the lesson by explaining the new topic.
Here 'объяснив' reflects the act of explaining the cause as a preceding activity to leaving the room.
Объяснив причину, она ушла из комнаты.
Explaining the reason, she left the room.
In this sentence, 'объяснив' signifies the act of self-reflection and clarification prior to making the decision.