运动 = exercise, He loves to exercise 他喜欢~~ An exercise in people power 民主权的~~ 健身 = fitness, literally things or activities to promote body health Body building and getting fit are two different things 健美运动与健身是兩回事 锻炼 = to temper, to forge, to toughen, to develop (one's skills) or to train oneself. This term comes from Chinese alchemy of making exlixirs etc. So you have the gold and fire radical. It is different from 練 to mean practise, exercise, to train in a non physical activity. For example, to study is 練书 and not 炼书!

Generally they mean the same thing if you want to express the idea that we make our body healthier by doing exercise. 你早上最好出去运动运动/锻炼锻炼/健健身。You'd better do some exercise outside in the morning. 多运动/锻炼/健身，少喝酒。Do more exercise and drink less. In addition, 健身is an Intransitive verb; 运动 and 锻炼 can be both transitive and intransitive, depending on the situation. Sometimes we use 运动 to simply mean "move our body parts" where we can't use 锻炼 and 健身 instead. 腿麻了，我起来运动一下。(you can't say 我起来锻炼一下 or 我起来健身一下 here) My leg has gone to sleep, I have to get up and move my legs a little bit. Normally we use 锻炼 to mean "strengthen our specific muscles " where we can't use 运动 or 健身. 多锻炼腿部肌肉，你才能游得快。(we don't say 多健身腿部肌肉 or 多运动腿部肌肉 in this situation) You can swim faster by improving and strengthening your leg muscles. However 运动腿部肌肉 means "move your leg muscles",which is different from "strengthen your leg muscles" 健身 literally means"make ourselves healthier使身体健康", there're many ways to achieve that goal, it doesn't necessarily to do high-intensity exercises. You might have heard of 打坐，you don't need to do anything but sit there and relax, that's what it's all about. 打坐健身（we don't say 打坐锻炼 or 打坐运动）

The difference between 运动, 健身 and 锻炼? 運動 has broader meaning to me; it means to do sports, to do exercise. (Broad & General term) 健身 sounds more specific, meaning the exercise that you do to shape the body; to work out (a kind of exercise; for specific purpose) 鍛鍊 is more like a written and formal words. Sounds like to train, to build up, to lick into shape, etc. Hope it helps.

It's hard to say, but I suppose 运动 means in a very general way, the purposes of 运动 could be various. There's a saying goes as 生命在于运动。生命 is at a general level, so 运动would be at the same level too. 锻炼 is more specific. And 健身 would be the most specific one，because it's usually used to indicate keeping in good shape physically.