This is the 17672nd most frequent Polish word.
zmagają
"Zmagają" means "they struggle" or "they contend."
Here, 'zmagają' indicates an active struggle against a challenging situation, specifically a flood encountered by the villagers.
Mieszkańcy wsi zmagają się z powodzią.
The villagers are struggling with the flood.
In this context, 'zmagają' implies a competitive endeavor where effort and determination are applied.
Sportowcy zmagają się w zawodach, aby zdobyć złoto.
The athletes are competing in the championships to win gold.
Here, 'zmagają' suggests intellectual effort and innovation directed toward solving a complex issue.