"Le piacciono i vestiti azzurri."
First, word order can be different in Italian than in English. In English, we almost always use Subject > Verb > Object (e.g. "She likes the dresses"), but in Italian, it can move around. Combine that with the fact that "piacere" is used to show who likes what, but literally translates as "to be pleasing" and it get confusing.
So think of the direct translation as "To her are pleasing the blue dresses" (sounds like something Yoda would say). Moved around into standard English, it becomes "The blue dresses are pleasing to her," or, more likely, "She likes the blue dresses."
I'm not very well-versed in Italian (yet, anyway), but that helps me understand it.