I think it's not entirely clear who it was built against (presumably some of the steppe tribes), but the archaeology of the wall, showing extensive and regular forts along the way, and the complex irrigation networks around it suggest that its primary purpose was in fact projecting an expansion of agriculture and the securing of state control over that area.
In essence, its best analogue would in fact be Hadrian's wall, where the goal of the wall was not to stop invaders, but to act as a deterrent and trade funnel for trading from the regions beyond the wall. The wall itself becomes a more intensively developed economic interaction zone. Consider too, that the most urbanized parts of western europe right now actually follow the FRONTIER of the Roman Empire, i.e. the legions and camps along the Rhine, rather than in the interior of the empire.
The more fascinating thing about the Gorgan Wall, which suggests a 5th-6th century CE construction in its current incarnation, is that the amount of state resources needed to fund it, suggests the Sasanid Empire had an internal bureaucratic cohesion on par with the Roman Empire, rather than the previously assumed adhoc aristocracy of before. And with that state cohesion, came (with Gorgan Wall as evidence) the possibility that the Sasanids actually could fund a sizeable standing army in the 6th century, which would explain their breakthrough ability during the wars with Phocas and Heraclius, rather than their usual raid and retreat pattern.
Source:
Oh yay another Hun question.
The Great Wall of Gorgan has quite a bit of mythology surrounding it. Some have connected it to Alexander the Great and the Caspian Gates, hence why the Islamic peoples called it Alexander's Wall. However, it's not actually mentioned for the first time until the 7th century, and for the longest time we didn't know when it was built until the first real excavations took place. The first dating was by Dr. Muhammed Kiani who in 1971 led a field expedition to survey the entire wall. Kiani attempted to date the original fortification as one that was built by the Parthian Empire probably in the 2nd century BC, and then re-built by the Sassanids after the 3rd Century AD. However, there's no real evidence supporting this. Using Optically Stimulated Luminescence, archaeologists dated charcoal, loess, and the kilns themselves and found the wall was probably built during the late 5th century AD.
Now, as to what enemy they were built against? I actually made a meme for that once: "When you're such a nuisance to civilized society that they build TWO walls to keep you out!"
That is, basically, the Huns.
Let me elaborate: There were many peoples moving through Central Asia in the 4th-6th centuries AD due to a series of megadroughts that had been brought on by the greater longer-period cyclic effects of the El Nino cycle. Most notably in 360, 430, and 550 AD. These dates more or less coincide with the movements of three people: the Xiongnu, the Hepthaltites, and the Eurasian Avars. The original Great Wall was united under the Qin and Han dynasties to keep the former, the Xiongnu, out. The Great Wall of Gorgan in much the same vein, was unified to keep out a people known as the Khionitai or Kidaritai, or Kidarites. When the Xiongnu aristocracy decided to start emigrating towards Europe in the 360's AD, another part of their state decided to push further into Baktria and Sogdiana, and came to be known as the Kidarites or Khionites (the latter word deriving from a variation of Xiongnu transmitted via Chinese and then through Sanskrit which became Sogdian Xwn and Ywn as well as Khyon, Khon, and Khionitai, among other forms). They came to be known as the Hunnashahs which survives via the 5th century Chinese form Wenna Sha. However, in the 430's-450's, the Hepthaltites (a people known formerly as the Hua, who were also associated with the Mulan story) were pushed by their Rouran overlords westward, and they started encroaching upon Sogdian and Baktrian Kidarite territory. The Kidarites retreated west until they were totally overtaken by the Hepthaltites in the 480's or so, but before then they had caused quite a bit of a problem with the Sassanids. The 450's-480's was about the time the Kidarites were in the region between Khwarezm and the Caspian sea (their capital's location is uncertain, some have put it at the Igdui-Kala fortress, but it was probably near Balkanabat or Turkmenbashi in Turkmenistan.) The Wall was probably built under Perozh from 459-484, although it was probably constructed out of a series of earlier forts in the region much like the original Great Wall, as well as Hadrian's Wall.
Which brings up a final point, these walls weren't actually built to keep peoples out. They hindered large armies and smaller raiding forces of both the Kidarites and the Hepthaltites (who were in Baktria and Sogdiana, but raided down into the Gorman plain and deep into Iran even), sure, but they didn't control migration very well. The primary purpose of these walls was basically to monitor, control, and tax trade across the border. This was true with the Gorgan, Hadrian's, and Great Wall.
Sources:
http://www.shca.ed.ac.uk/staff/supporting_files/esauer/iranian_walls.pdf
https://www.jstor.org/stable/4300707?seq=1#page_scan_tab_contents
Also check out my post on the Hepthaltites for more about them.
Oh I should mention the Sassanids actually did build a fortress at the Caspian Gates as well as another one at the Iron Gates (called Iouriepaakh by the Romans), also to keep Huns out (the Xailundur/Xailiandur, Brjan, Mask'ut, and Barsil Huns a.k.a. the various "Caucasian Huns"). So technically we built three walls to keep the Huns out. Four if you count the Theodosian Land Walls. Hell five if you count the re-fortification of the Danube by Theodosius II in 444-445.
They were REALLY annoying.