From what I have read, there's no clear consensus. Most cite that it is a safety feature, helping to prevent the knife from shutting on one's fingers. Some assert that it reduces the wear on the spring to some degree, but I don't know if I buy that given that the spring spends the same amount of time under tension when opening, with either a rounded tang (no half stop) or a flat tang.
To some degree, I could see how a half-stop would make a knife safer as it aged or if it became loose at the pivot. A blade that swang freely when not in the fully open or closed position would be a real hazard, and a half-stop would ensure some measure of controlled closing regardless of pivot tension.
Edit: From a material physics standpoint, a square tang engages a significantly smaller amount of the tang to the spring. Almost the entirety of a rounded tang will meet the spring, whereas a square tang only engages the corners of the tang against the spring.
Additionally, there is some speculation that it was a safety measure brought about by older slipjoints having very strong backsprings, which made the half-stop a bit of a safety feature in that you had a halfway point to prevent the knife from snapping shut with force if your fingers were to slip, or if you were careless, etc.
Edit II: They can also act as a bit of a self-cleaning feature, as the tang of the blade scrapes against the spring (instead of sliding along it) which can help prevent / remove gunk buildup.