Learn French: Elles sont mariées depuis dix ans. - They have been married for ten years.

Because it is used with the verb être (to be). The word marié acts like an adjective here and has to agree with the subject Elles (they, feminine). You add an -e for feminine and an -s for plural, making it mariées.

Why does the English translation say 'have been', but the French uses sont (are)?

In French, if a state or action started in the past and is still continuing in the present, you use the present tense. Because they are still married right now, French literally says 'They are married for ten years.' English requires the present perfect tense ('have been') for this, which doesn't translate word-for-word into French.

Why use depuis to mean 'for'? Shouldn't it be pour?

This is a classic trap! When talking about an ongoing situation up to the present, depuis translates as both 'since' (a starting point, like 2010) and 'for' (a duration, like ten years). You almost never use pour for past durations in French; it is mostly used for planned future time, like 'I am staying for a week'.

Do I pronounce the extra -es at the end of mariées?

No, it is completely silent. The words marié, mariée, mariés, and mariées all sound exactly the same out loud! The extra letters are only there in writing to match the feminine plural subject.