"La festa è iniziata ieri."
Traduzione:The party started yesterday.
I try to explain it. In Italian some verbs are transitive, some are intransitive, some may have both of the forms. "Iniziare" belongs to the last group. When "iniziare" is used as a transitive verb it means that "someone begins to do something" while when "iniziare" is used as an intransitive verb it means that "something begins". In Italian compound tenses, they take different auxiliaries: the transitive form takes "avere" , while the intransitive form takes "essere".
"Iniziare" also takes "essere" to form all the tenses of the passive form.