Round pens are small scale mobile arenas. Some are square, some are round. The NH movement brought a "pen, training lot, breaking pen, corral and assorted other terms " into the limelight as a round pen.
It's a great way for those of us without an arena to still have the option to free lunge a horse, train at liberty, teach directional changes while free lunging using only non verbal/body position, emergency quarantine/dry lot, holding pen, etc.
Their biggest draw to me is mobility, if you use the panels to create one. It can be dismantled and moved by a single person. It doesn't take a degree in physics, a truck load of tools, carpentry skills, or a super amount of strength to assemble/disassemble. A panel can be used as an emergency gate. Remove one, fasten to gate posts, drag the others closed, re-pin and go back to working your horse until you can replace the gate. They make awesome temporary pastures and the mobility means you can rotate in a flash. Unpin the panels, drag where needed, re-pin and poof fresh grass. Temporary sectioning of pastures is another plus.
Changing the shape is another plus. It's easier IMO to teach a horse to turn to me, rather than away, when there is no corner for them to run to. Yet if I need to teach a little more bend in the corners, drag panels and make a square or rectangle. It all depends on my needs at the moment. *shrugs* They are versatile. Anything I can get multiple functions from, for the price of panels, is a plus in my book.
"Light travels faster than sound. That's why some people appear bright until you hear them speak."
Larry the Cable Guy