it's really just a weight limit. The swing will tell you the restrictions. As far as age - my son enjoyed it about the first month of life. He had a Graco Soothing Center and would only sleep in there. After the first month, he hated it LOL. And after the first few months, he'd fight his way out of it or scream if he couldnt figure out a way to sit up in it and try to climb out.
SOme babies are cuddlers and like to be rocked - and that they may never grow out of! They would enjoy a swing much longer than a different baby who, for instance, can't sit still and constantly wants to move and explore. Just depends!