Learn Spanish (Latin America): Ella es más delgada que su hermana.

In English, we often add "-er" to the end of short adjectives to compare things (like "thin" becoming "thinner"). Spanish doesn't have an "-er" ending. Instead, you put más (more) before the adjective. So, más delgada literally translates to "more thin".

Does delgada have to match the person it describes?

Yes! Because the sentence is about Ella (she), the adjective must be feminine, which is why it ends in -a (delgada). If we were talking about a man, it would be Él es más delgado.

I thought que meant "what" or "that". Why is it used here?

Que is a very versatile word. When you compare two things using más (more) or menos (less), que acts as the word "than". Notice that it doesn't have an accent mark here, unlike the question word ¿qué? (what?).

Why is it su hermana for "her sister"? Doesn't su also mean "his" or "your"?

Yes, it does! Su is a flexible possessive word that can mean "his", "her", "your" (formal), or "their". Because we are already talking about Ella in this sentence, the context makes it clear that su means "her" here.