It might be a passive fire protection measure.
While the ceilings between floors are fire rated, fires can easily spread through the windows along the outside façade. (Coanda effect will pull the flames towards the building)
The ledges push the plume away from the building.
They may be part of architectural features. They can be an attempt to cover up some structural tie-beams or retrofit work ordered by the building authority.
Or they could be some kind of window awning to provide shading.
They certainly weren't designed for parkour heroes jumping around on them.