A sombrero is a Mexican hat: tall in the middle, with a very wide round brim that often curls up a little at the edge. It is made to keep the sun off — not just your face but your neck and shoulders too, which is why the brim is so wide. Real working sombreros are usually straw, plain and practical, worn by farmers and by horsemen. The ones foreigners picture are the fancy kind: huge, decorated with silver thread, worn by mariachi musicians. That gap matters. In English, 'sombrero' has become a costume word — you meet it at parties, in cartoons, and in the sentence 'someone in a giant sombrero'. Because of that, it is easy to use it in a way that reduces a whole country to a hat, and Mexicans are quite reasonably tired of that joke. So use the word for the actual object, and be a little careful with it as a party prop. One nice detail: in Spanish, sombrero just means 'hat' — any hat at all. A baseball cap is a sombrero in Spanish. English borrowed the word and made it narrow, so that it now names only the one style Spanish speakers would call a sombrero mexicano or sombrero charro. The plural in English is sombreros.