In both Amherst and the Town of Tonawanda, these drainage systems take the gutter water from the house, out to the storm sewer that runs underneath the street. The vents near the curb are there to allow the rain water coming from the house a place to go when the storm sewer is too full to take the water, or just can't take if quickly enough. These are commonly called bubblers, as the water bubbles out of them when the sewer is full. Commonly, there are leaves, tree, roots, mud, etc. that can clog up the pipe. I was able to use a shop vac to clean out the water from the pipe, and then tried using a snake to get through to the sewer. This didn't help, so I called the town of Amherst. They sent out a truck that cleans out the connection via water pressure. It worked fine for about six months, and then was filling up with water again. I called again, and they replaced the vent and connection to the sewer, as it was their responsibility. It was pretty much plugged solid with mud.
Best thing to do would be to call the town and see who is responsible for it.