This is the 262nd most frequent Polish word.
powinny
"Powinny" means "should" or "ought to" (used for plural subjects).
The word 'powinny' is used here to express a recommendation or requirement for plural noun 'dzieci' (children).
Dzieci powinny jeść zdrowe jedzenie.
Children should eat healthy food.
Here, 'powinnyśmy' is used in a question form, specifically addressing a group of speakers, all female, as 'we' intending necessity or advice.
Czy powinnyśmy zacząć od początku?
Should we start over?
In this sentence, 'powinny' is accompanied by 'były' to indicate a past expectation or assumption for action related to plural feminine or neuter subjects.