Answer: Those symbols (« and ») are angular quotation marks, often known as chevrons or guillemets, comillas franceses or comillas angulares in Spanish. They're interchangeable with and are used the same way as are regular double quotation marks. They are used much more in Spain than in Latin America, possibly because guillemets are commonly used in various non-English European languages such as French.
Quote marks of either the angular or regular variety are used much as they are in English, most often to quote from someone's speech or writing or to call attention to words that are given a special or ironic use. The main difference from American English is that added commas and periods in Spanish go outside the quote marks, while in American English they go inside the quote marks. A pair of examples shows how these marks are used:
- "Ninguna mente extraordinaria está exenta de un toque de demencia", dijo Aristóteles. / «Ninguna mente extraordinaria está exenta de un toque de demencia», dijo Aristóteles. "No extraordinary mind is free of a touch of insanity," Aristotle said.
- Tengo una "hija". Tiene cuatro patas y maulla. / Tengo una «hija». Tiene cuatro patas y maulla. I have one "daughter." She has four legs and meows.
Keep in mind that it is extremely common when printing dialogue in Spanish to dispense with quote marks entirely and use a long dash ( — ), sometimes known as an em dash (raya in Spanish), to indicate the beginning and end of the quotation or a change in speaker. It isn't necessary (although it's often done) to start a new paragraph for a change of speaker, as is usually done in English. No dash is needed at the end of a quotation if it is at the end of a paragraph.
- —¡Cuidado!— gritó. "Careful!" he shouted.
- —¿Cómo estás? —Muy bien, gracias. "How are you?"¶"Excellent, thank you."
- —Si quieres tener amigos— me decía mi madre—, sé un amigo. "If you want to have friends," my mother told me, "be a friend."