This is the 4595th most frequent Russian word.
губернатором
"Governor" (a regional official).
In this sentence, 'губернатором' is the instrumental case of 'губернатор' (governor), indicating Peter's role or title after his appointment.
Пётр был назначен губернатором этого региона.
Peter was appointed as the governor of this region.
'губернатором' is again in the instrumental case, here used to describe the person with whom the meeting was held.
На встрече с губернатором обсуждались важные вопросы.
At the meeting with the governor, important issues were discussed.
The word 'губернатором' in this context indicates the role or position held while performing the described actions.