What architectural roofing feature is this?
The building feature that you have indicated in your picture is designed in this case to provide an overhang over the front sidewalk. In this case the overhang provides cover during rainy conditions for persons coming to and leaving the business. Similar style overhangs such as this are also used for:


adding a false front to the building to make it look like a bigger building that it really is.
hiding unattractive heating and cooling equipment that may be mounted on the roof of the building so that it is not visible from the front.
Producing a prominent space to display the business name.


Often overhangs like this are built out from the face of the building and not tied into the original flat roof structure of the building. In these cases it is a lot easier to re-roof the original structure of the building and then separately address the roofing of the overhang unit and any flashing that deals with diverting water from the overhang onto the original roof. 

In cases where an overhang like this is built up quite a bit higher than the original roof then it may be tied into framing that attaches into the original roof and cantilevers over the edge. This can make for a much more complex job in re-roofing the building. 

As far as removal it will depend on a number of factors some of which include:


If the owner of the building wants to eliminate the overhang.
Need to evaluate if this overhang was added onto the original building structure after the fact.
If the overhang framing is integral to the original roof structure it could be a big added job to remove the cantilever framing and patch the original front roof edge.
The type of construction used for the overhang can be a driving factor for removal. For a plain wood facade it can be easier to remove than something covered in stucco as you indicated that this one is finished with.