Badajoz /ˌbɑːdəˈhoʊs/ noun2 •A city and municipality, the capital of the province of Badajoz, Extremadura, Spain.It was at this town of Badajoz, the capital of Estremadura, that I first fell in with those singular people, the Zincali, Gitanos, or Spanish gypsies. — 1843 •A province of Extremadura, Spain, around the city.