This street makes a rather conspicuous cut through an otherwise elevated, stone-encased stretch of the now-defunct Old Croton Aqueduct (the southern portion of the severed aqueduct embankment is visible above). As you might suspect, Burnside Avenue did not exist at this location when the aqueduct opened in 1842. For 50+ years, the water traveled through a pipe inside a continuous man-made ridge here, with no roadway interrupting its progress.
Sometime around 1897, Burnside was extended westward through the path of the aqueduct, and a bridge was constructed over the street, carrying a conduit that allowed the water to continue south on its elevated course while vehicular and pedestrian traffic passed beneath it through a set of stone arches. A few decades later, Burnside was widened, and the bridge was replaced with an inverted siphon that routed the aqueduct below the roadway, creating the bluffs-on-a-river appearance that has existed here ever since.
In researching this crossing, I found an old photo that sheds some light on the history of a very small and very strange-looking vacant building that stands at the northeast corner of Burnside and University, adjacent to the aqueduct, and just to my right in the photo above. I didn't get a good shot of it, but between my lousy picture and this bird's-eye view, you can get a decent idea of what the place looks like. I'm not sure if this structure originally had some function related to the aqueduct, but, thanks to this photo from the NYPL's historical image archives, I do know that it served as a Tydol gas station during the 1930s. (You can also just make out a "GAS" sign on the building in this image from the 1920s.)