Linguistically, the Sumerians major contribution was the cuneiform script, one of the earliest forms of writing, which was subsequently adopted by the Semitic people who later supplanted them.
The Sumerian language, at least back when I was a student and perhaps still, could not be related to any other known language.
The Sumerians formed competing city states in southern Mesopotamia that were continually at war with one another for political dominance, until they were all finally conquered by the Akkadians, a Semitic people, under Sargon the Great. The Akkadians had already adopted the cuneiform script.
With the conquest the Sumerians appear to have largely died out probably through assimilation, though their language and legends persisted long after Sumerian had disappeared from common speech.
The following websites might be helpful to you, along with the works of Samuel Noah Kramer, such as The Sumerians: Their History, Culture and Character.
One more thing, after sumerian was no longer a spoken language, it was still used for centuries for religious matters. More or less like Latin is used today by the Catholic Church.
As for linguistics, not only sumerian was one of the reasons archaeologists swarmed to the middle east during the XIX century to find new texts, but it also created great debate on ancient languages during that same period, boosting linguistics to new heights.