Your question intrigued me, and so I decided to do a little research. Generally, it is unknown exactly where the Sumerians came from, as most of what we know of them as a distinct culture comes from the texts they wrote.

After wading through a bunch of crazy people talking about how they were Africans, aliens, asians, who knows what, I found a blog by someone who makes some very interesting claims and cites a lot of scholarly articles. He suggests that the "black-headed people" were a foreign elite who invaded and imposed their language on the semitic-speaking local populace. He suggests that they were called "black-headed" because they wore their hair long and wore beards while everyone else tended toward shaved heads. He uses a bunch of cylinder seals and other artistic depictions of people from the Uruk period, and the people depicted as having hair are depicted as larger, often holding weapons, and are more heavily clothed. This may indicate that the "black-headed people" were referred to as such because of their hair.

Here is a link to the post: http://armchairprehistory.com/2011/08/10/the-black-haired-sumerian-elite/

Now, understand that this blog author has not published any of his work, and is not part of the academic community, so take this explanation with a grain of salt.

However, what scholars do know is that Sumerian is a language isolate, meaning it is unrelated to any other known language, modern or ancient, and therefore it has been argued because of this that the Sumerians are not native to Mesopotamia, since all the other languages of that region have been derived from the Semitic language family. It is possible that the Sumerians were from Mesopotamia somewhere but were self-sufficient enough that their language formed independently of the Sumerians.

However, the nature of loan words in Sumerian and Semitic language such as Akkadian, this blogger argues, indicate that Semitic was the technical language, as there are more Semitic loan words in Sumerian than the other way around. This may indicate that the Sumerians laid their culture and language as a veneer over the existing Semitic culture of the region.

However, we don't really know one way or the other. I think this is a plausible argument, but I'm not an expert on the Uruk and Ubaid periods in Mesopotamia, so please do take this with a grain of salt.

It's a much better idea than trying to conclude that it meant they were from Africa.