A brougham is an old kind of horse carriage: four wheels, a closed roof, and a horse (sometimes two) pulling it. The driver sat outside at the front; the passengers sat inside a small, neat box, out of the rain. It was a city carriage more than a farm wagon — the sort a well-off person used in the 1800s to go about town. You will meet the word in history, old novels, and museums, not in ordinary talk; most people now just say carriage. Though actually, the name later stuck to some early motor cars with the same shape (closed in the back, the driver more open), so you may see it on a vintage car as well as on a horse-drawn one. It is named after a British politician, Lord Brougham (1778–1868), who rode in one and either invented the style or made it fashionable.