This is the 11124th most frequent Polish word.
gestem
"Gestem" is the instrumental case of the Polish noun "gest," meaning "gesture."
In this sentence, 'gestem' means 'with a gesture' and refers to using physical movement to convey agreement.
Pokazałem gestem, że się zgadzam.
I indicated with a gesture that I agree.
Here, 'gestem' signifies 'using a gesture' as the means of communication when verbal interaction isn't possible.
Rozmawiałem z nią gestem, bo nie znała naszego języka.
I communicated with her using gestures because she didn't know our language.
In this usage, 'gestem' relates to the specific action of reaching out with a hand to signify harmony or agreement.