This is the 5070th most frequent Russian word.
мнениями
"Мнениями" means "opinions" (instrumental plural form).
In this context, 'мнениями' is the instrumental plural form of 'мнение', used to express what was being exchanged.
Мы обменивались различными мнениями о событии.
We exchanged different opinions about the event.
Here, 'мнениями' is used in the instrumental plural form to indicate what participants shared.
На конференции участники поделились своими мнениями.
At the conference, participants shared their opinions.
In this sentence, 'мнениями' functions in its instrumental plural role to define the action of exchanging opinions.