Annoncer is one of those verbs whose meaning is so apparent that teachers expect to you to recognize it when you see it. Obviously it means "to announce"!
But when annoncer is reflexive (s'annoncer) it takes some thought to translate it properly into English (something "announces itself" won't work). Consider these examples:
La journée s'annonce difficile. It looks like it's going to be a hard day.
Le temps s'annonce beau. The weather promises to be nice.
La moisson s'annonce bien belle. The harvest looks promising.
L'été s'annonce chaud. It looks like we're in for a hot summer.
La saison s'annonce bien. The season is off to a good start.