Can you explain the difference between “mi piace” and “mi piacciono” in Italian?

A couple of examples:

Le scarpe mi piacciono. - I like the shoes. (The shoes please me.)

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Contrary to English “I like it", “mi piace” is not a personal expression with “I" as the subject. In Italian the subject and object are transposed — “mi piace" literally means “it pleases me". The verb is third person singular.

The direct object pronoun “mi" is the object of the verb “piacere" (to please). Also known as conjunctive, such pronouns generally precede the verb that governs them. The expression “mi piace", employing third person singular format, translates literally to English as “it (understood) pleases me", i.e. I like it.

La veste mi piace. - I like the dress. (The dress pleases me).

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From discussion thus far you might already have understood that “mi piacciono" employs the third person plural form of the verb and translates as “they (understood) please me”, i.e. I like them.

The endings of verbs indicate person and number in Italian and subject pronouns may therefore be omitted except when necessary for clearness or emphasis. In the case of “it" and “they" (referring to things) they are almost never used.