I wanted to answer just that. By checking for change in the state of the key (ie from up to down or vice versa) you can implement snappier controls. In your case, you could have made the player move right only when the key was just pressed, but not move if key is pressed but was already last time you checked.
I don't know which tools you used to make your game, but a lot (if not all) game engines should have a "GetKeyDown" function or something equivalent, which does just what we discuss.
Hope this helped you, and have a great day!