Learn Spanish (Latin America): ¡Cállate, por favor!

Because this is an affirmative command (telling someone to do something). In Spanish, object and reflexive pronouns like te must be attached directly to the end of affirmative commands. If it were a negative command (telling someone not to do something), the pronoun would go before the verb: no te calles.

Why is there an accent mark on the first 'a' in cállate?

When you attach a pronoun to the end of a command, you add an extra syllable to the word. The written accent mark is added to keep the spoken stress on the exact same vowel as the original verb (calla).

Why do we use the pronoun te here instead of just saying calla?

We are using the reflexive verb callarse (to keep quiet or shut up). Since we are giving a command to someone we address as tú (the informal 'you'), we use the matching reflexive pronoun te. While calla is sometimes used, cállate is much more common in everyday Latin American Spanish.

Is cállate polite since it includes por favor?

Not necessarily. Cállate is an informal command and can sound quite harsh, often meaning something closer to 'shut up'. Adding por favor softens it a little bit, but it is still a very direct and forceful thing to say!