Piacere is the direct translation of to like, but this verb doesn't work like its English counterpart.
Gli, le are contractions of to him, to her. While English begins the sentence with a subject, Italian uses a so called "complemento di termine". If you studied a language that has declensions, you can relate this complemento di termine to the dative case, answering the question "to what, to whom?".
Gli piace / gli piaceva = a lui piace / a lui piaceva
Le piace / le piaceva = a lei piace / a lei piaceva
Literally translated, it means "to him like, to her like". What's different here is that there's nobody who likes something, but an X thing is pleasing to somebody.
In the sentence "le è piaciuta", that le refers to the person who likes this X thing, not to the X thing itself:
Le piace quella giaccia. She likes that jacket.
Gli piace quella giacca. He likes that jacket.
Le piace. She likes (it).
Gli piace. He likes (it).
The object of the sentence (the "it", which in Italian is called "complemento oggetto" and answers the question "what, who?") is not related to gli/le. Gli/le refers to the person.
This "complemento di termine" can open a bunch of other sentences, such as:
Vi scrivo una lettera. I write you (all) a letter.
To you (all) I write a letter.
Le ho detto di preparare la tavola. I told her to set the table.
To her I told to set the table.
To differentiate between the complemento oggetto and the complemento di termine, ask yourself which part of the sentence answers to "to whom?" and which one answers to "what?".
Le ho dato un fiore.
Le (to her) ho dato (I gave, subject) a flower (what did I give her? a flower).
Piacere is a special verb in Italian, in that the thing that is liked is the subject, and in that the English subject (the person liking X thing) is rendered as a complemento di termine (to the person).
Le piace quella giacca = Quella giacca le piace = Quella giacca piace a lei
We could try translating it as: That jacket is pleasing to her. But don't rely on the English syntax too much (as I'm doing to illustrate the differences...) when learning these special verbs.
And I was almost forgetting: since the English object is here the subject, the verb is conjugated according to it:
Il fiore piace alla donna. "The flower is pleasing to the woman".
I fiori piacciono alla donna. "The flowers are pleasing to the woman".
Alla donna piace il fiore > Le piace il fiore
Alla donna piacciono i fiori > Le piacciono i fiori
Le piace quella giacca. "That jacket is pleasing to her". She likes that jacket.
Le piacciono quelle giacche. "Those jackets are pleasing to her". She likes those jackets.
This construction is unfortunately unknown to English and I hope I didn't make the topic too much confusing. If you have other questions, don't hesitate to ask!