This is the 1602nd most frequent Russian word.
тренером
The Russian word "тренером" means "coach" or "trainer" (instrumental case).
The word 'тренером' is used in the instrumental case to indicate the role or occupation (coach/instructor) of the subject after becoming it.
Я стал тренером по плаванию в прошлом году.
I became a swimming coach last year.
The word 'тренером' is used in instrumental case as part of the structure 'познакомиться с кем-то', meaning 'to meet someone', specifying 'coach'.
Вчера я познакомился с тренером чемпионской команды.
Yesterday, I met the coach of the championship team.
Here, 'тренером' is instrumental case used to specify 'coach' as the item of pride of the subject.