Play streets — blocks of local city streets that are closed off to vehicular traffic during certain hours to give kids a safe place to play — date back to at least 1915. You can see old photos of play streets here and here.
Play streets currently seem to come in two distinct varieties. Summer, or community, play streets operate during the, well, summer, mostly "in neighborhoods where money and open space are scarce. Play streets often serve children who cannot afford day camp, much less sleep-away adventures." School play streets, on the other hand, operate during the school year and provide extra recreational space for "schools with limited or no access to a gymnasium, multi-purpose space, or outdoor recreation facilities."
Here's a short video of a summer play street in action. The kid at 0:36 just can't restrain himself.
The sign above is located outside an elementary school (PS 55), but it looks to me, based on its hours, like it's for a summer play street. (If that is indeed the case, I have no idea what it's doing on the sidewalk here in January.)