This is the 336th most frequent Ukrainian word.
будинків
"Будинків" means "houses" (genitive plural form) in English.
The genitive plural form 'будинків' is used here to describe the possession or attribute that the city has; it is full of buildings.
Місто було повне великих та сучасних будинків.
The city was full of large and modern buildings.
In this sentence, 'будинків' is the genitive plural and indicates possession, referring to the owners of the houses.
Власники будинків повинні слідкувати за їх станом.
The owners of the houses must monitor their condition.
Here 'будинків' is also in the genitive plural, describing part of a whole, indicating that some buildings from the total were affected.