Young families and old residents come here on sunny days and feed the ducks. The pond has a rich birdlife, though questions have been raised on the future of it as the seagulls have made themselves way to friendly there.
You'll most definately end up there at some point. Walking around the pond on a lovely day is great way to begin or end a day in the city. Bring a loaf of bread for the ducklings and then have a seat at the "Við tjörnina" coffeehouse.
I wouldn't recommend swimming in it, as it is both quite shallow and dirty.