So far as we know at this point in time, our species, Homo sapiens, originated on the continent of Africa. To be more specific, we believe that the species originated in the eastern part of that continent. We have at least two threads of evidence that support the idea that Homo sapiens evolved in Africa.
First, we have fossil evidence. Fossils that have been found in East Africa are the earliest that can be (in paleontologists’ interpretation) classified as anatomically modern humans. Fully modern humans appear to have been living in East Africa at least 120,000 years ago. There is no evidence of fully modern humans outside of Africa or its immediate vicinity until about 60,000 years ago. Thus, as far as we know from fossils that have been found so far, Homo sapiens originated in East Africa.
Second, we have genetic evidence. Scientists have used DNA analysis to hypothesize that all humans today are descended from a woman who lived about 200,000 years ago in Africa. While not all DNA evidence is conclusive, it appears that DNA also points to Africa as the origin for our species.
The evidence points, then, to Africa (and specifically East Africa) as the place where Homo sapiens originated.