Most of the time I see people using it to practice combos, techs for their character, or labbing out percent bands or frame tolerances for various move combinations.
An example of this would be something like this:
Ridley has a combo you can do where you grab somebody, down throw them, short hop into a neutral aerial, and then fast fall, dash, and grab them again. Since I main Ridley, I may want to practice this, and the opportunities to do so during an actual match may not present themselves frequently enough for me to get good training and practice in on this specific thing.
I may enter training and try to practice doing this against a CPU to get the button timings down. I can use the combo tracker to see if I'm landing my neutral air too late, as if it doesn't go up to "2" when I hit with nair, I know they could've air dodged and evaded my combo attempt. Figuring out if you're grabbing soon enough is a bit more annoying, as the CPU 'shuffle' option doesn't seem to work, but you can get the general idea here.
There's a lot of stuff you can do in the training room to try to better your game, and the above is just one example. Most of the time you can visit either the character forums or the character-specific discords to figure out what would be useful to do in the training room.
https://docs.google.com/spreadsheets/d/1SMQBjv2T_QKkTr6VJzr9FBSoMzHz9bU-cKcYSauker4/edit#gid=0
Here's a whole bunch of stuff from the Dedede discord.
Here's some random thing I picked off of it:
"Between 28% and 40% Dedede down throw to RAR back air, creates easy jab lock scenario (Kills above 33% if they miss the tech)"
You may want to practice this, for example, in the training room. Put a CPU between these percentage bands and try practicing down throwing it into a RAR back-air, and then into a jab lock. I've done similar kinds of things for various Ridley stuff.
