This is the 822nd most frequent Russian word.
появились
"Appeared" or "emerged."
In this sentence, 'появились' refers to the stars emerging or becoming visible in the sky after previously not being observable.
Вчера на небе появились звёзды.
Yesterday, stars appeared in the sky.
Here, 'появились' describes the arrival or introduction of new neighbors to the neighborhood unexpectedly.
У нас вдруг появились новые соседи.
We suddenly got new neighbors.
In this case, 'появились' means that ideas were generated or came to mind as a result of the discussion.