Learn Spanish (Spain): ¿Les gustan los sellos españoles o las fotos?

In Spanish, gustar works differently than "to like" in English. It actually means "to be pleasing to". The things being liked—the stamps (los sellos) and the photos (las fotos)—are the real subjects of the sentence. Because these items are plural, you must use the plural verb form gustan ("are pleasing").

Who exactly does "les" refer to?

Les is a pronoun that means "to them" or "to you all" (formal). The translation shows "Do they like...", but depending on who you are talking to, this exact same sentence could also mean "Do you all like Spanish stamps or photos?".

Why is it "las fotos"? Doesn't the "o" at the end mean it should be masculine ("los fotos")?

It is an exception! The word foto is short for fotografía, which is a feminine word. When Spanish speakers shorten feminine words like this, they keep the feminine "the", which is why it stays as las fotos.

Why does "españoles" have an "es" at the end, and why is it after the noun?

In Spanish, describing words (adjectives) usually come after the thing they describe. Also, they must match the noun in gender and number. Since sellos is masculine and plural, español needs to match it. Because español ends in a consonant, we add -es to make it plural, creating españoles.