You may know of a brogue as a thick Irish accent, and that can help you remember another meaning: it's also a thick Irish shoe.
Brogues are heavy, sturdy Irish shoes, and they're usually made from untanned hide. This is a working person's shoe: it's definitely not a fancy shoe or dress shoe. Brogues can also be called clodhoppers or brogans. If someone's coming from behind you in brogues, you're likely to hear them. It's almost impossible to tiptoe in brogues.