It's a bit of an odd duck. I rarely see anyone there, which isn't that surprising, because it doesn't look particularly inviting. There are some residences and offices nearby, but there are nicer open spaces that are as close or just a little bit farther from the plaza. There's a bit of a lake view from there, but anyone who wanted to look at the lake would just walk the extra block to the lakeshore. I've visited it once or twice while waiting for a bus, but there was nothing there to explain why a plaza had been placed in this particular spot. Finally, I just chalked it up to a failed experiment in urban redevelopment.
Earlier this month, though, I figured it out. Well, not so much figured it out as obtained the missing piece of information that made it clear. It was July 4, and I'd missed the last bus, so I was walking home from downtown. Part of my route took me along the shore of Lake Monona, and when I looked to my left I got a glimpse of the other side of the plaza. It turns out that the plaza is, in fact, the roof of a building.
Specifically, the roof of one of the City of Madison's water wells. It's not just a weird little plaza; it's the city cleverly making something moderately useful out of something that would otherwise be an eyesore along one of the main routes out of the downtown area. That's much better than a failed urban redevelopment scheme!