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

Thank you for your question.

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.

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.

Astronomers see the 1st stars dispel darkness 13 billion years ago at 'Cosmic Dawn' - Space

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.

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.

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

A reservoir of gold lies hidden in Earth’s core. Scientists say it’s leaking - CNN

A couple of examples:

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