It's just a subtle change in the meaning, leaning more towards modify or revise than change, perhaps.
- You can ændre something, someone, or yourself (change).
- You can only ændre på something (modify, revise).
- You can also ændre ved something, which has the sound of do something/anything/nothing about: Det kan der ikke ændres ved means nothing can be done about that.
Danish likes to form phrasal verbs using tiny words that modify the meaning ever so slightly :)