When something is run-down, it's in poor condition from not being taken care of properly. A run-down building might have peeling paint, broken windows, and weeds growing through cracks in the sidewalk. A run-down neighborhood has houses and stores that need repairs but haven't gotten them. The word suggests gradual neglect rather than sudden damage: things have slowly gotten worse because no one maintained them.

People can be run-down too. When you're feeling run-down, you're exhausted and worn out, like a toy with dying batteries. You might feel run-down after staying up too late several nights in a row, or after pushing yourself too hard without enough rest.

Notice the hyphen: run-down (with a hyphen) describes something's condition, while run down (two words, no hyphen) means to chase and catch someone or something, or to speak badly about someone.