Used before a noun to describe a building that is old, broken, and slowly falling apart — walls leaning, roof with holes, no one taking care of it. It comes straight from the phrase 'tumble down', meaning to fall down, so the picture inside the word is a house that is halfway through collapsing. It is almost always used about buildings: a tumbledown cottage, a tumbledown barn, a tumbledown wall. Two things worth telling your students. First, it is a slightly literary, storybook word — you meet it in novels, travel writing, and estate-agent language more than in daily speech. Second, and this is the interesting part, it is not purely negative. English has plenty of ugly words for a broken building; 'tumbledown' often carries a touch of charm, the kind of ruin a painter would want to paint. A 'tumbledown cottage in the hills' sounds romantic. A 'derelict building' does not.