We use our round pen for free working horses, as a controlled area to start or work green horses, a smaller contained area for lessons where horse or rider may be do distracted or not coordinated enough to be in indoor or outdoor arena.
The round pen is great with a young horse that has no forward. The rider can focus on forward instead of a specific direction. It's also a great area to collect a horse. The smaller diameter can enable a ride to keep the horse together instead of letting them get strung out in a larger area.
Also nice to start teaching a horse to move over objects as they have less room to avoid them.
We also have used it as a quarantine pen for new arrivals. Ours is situated between the barn and indoor arena with the outdoor running down one side. Sheltered and yet the new horse doesn't feel so lonely.
+1 -- We don't have a indoor. The ring is a great tool. This is their first home when we get new horses on the farm. Especially ones that have not been pastured and on grass.
The ring has been Big Blacks home since we brought him home. The previous owner had him on a hay and sweet feed diet due to their lack of pasture. We are slowly getting him back on grass.