This is the 13475th most frequent Russian word.
направились
"Set off" or "headed" (past tense, plural).
In this sentence, 'направились' is used to indicate the act of setting forth or moving towards a destination, in this case, the city center.
Мы направились к центру города на автобусе.
We headed towards the city center by bus.
Here, 'направились' describes the action of departing toward a location, specifically the park, for an intended activity (a walk).
После обеда они направились в парк на прогулку.
After lunch, they headed to the park for a walk.
In this example, 'направились' conveys the idea of moving with purpose towards the library, indicating intent and direction for exam preparation.