Sparsely means only occassionally or thinly. So, sparsely settled means people occupy the space, but spread out. Example: The sparsely settled colony of 5000 square acres only had 40 residents, with most of them living in town and some living on the outskirts.
In the late 1800s most immigrants that were coming to the United States settled in the area now known as New York City and Manhattan. Immigrants that came from Asian decent settled along the west coast.