When you perform a pull-down, your target muscles are the latissimus dorsi, a pair of large muscles behind and beneath your armpits. Hence you get the "lat" in "lat pull-down."
Think about that particular muscle as you pull the weight down with each arm. Focus on it, flex it, use that mind-muscle connection, and you'll feel it tomorrow. It's easy to just move your arms to pull the cables down, but that's not the point. If you want your back to get bigger and wider, your lats need work. Think about your back, use your back, and it will do what you command.