Training mode is good for practicing simple things like movement, spacing, shield dropping, ledge hugging (also known as "speed snapping" and "manual ledge snap"), jab cancelling (if it's applicable to your character), and even power shielding if you use a level nine pikachu, mario, villager, ect.
You can practice those things and more in a controlled environment without the pressure of an opponent's interference. This is pretty good for developing muscle memory, especially if you're willing to do drills.
At the very least, you could just use it for warm-ups before you start playing matches.
Also, be careful about ever using the CPU. It has some niche uses, but try to avoid the pitfall of simply beating the computer up; it's a great way to develop terrible habits.
Sometimes I'll use it to test air dodge traps against landing/airborne opponents because it usually appears to always time an air dodge so the first frame of invulnerability overlaps the first active frame of your attack, so you can test which moves can outlast an air dodge (Like Bowser's N-air for example) or your options after forcing an air dodge to the ground. The computer will typically always at least shield or dodge when it can but I recommend multiple repeat tests and/or testing with a training partner to be sure. Tests done with a partner and even the 1/4th solo training mentioned before are generally always better than the cpu if you have the option.
Anyway, that's just my approach to training mode; hope it helps!