This is something Im always confused about. We accept that this was the Roman Empire, but what determined this in their time? Did they just lay claim and say, "Everything up to this river is ours?" Did the people even know they were "roman"?
Or was it a more practical reason? Like they had military forces in this area?
Or are these borders sort of made up but us? That historians kind of "fill in the bubbles" to show the empires actual influence. But that those in their time didnt view the borders this way.
The Romans didn't have an actual concept of a "limit" to their empire - in their own view the empire was endless, there simply were areas that weren't Romanized.
The Romans denoted their borders or "limes" usually by a ditch, or a system of defensive fortifications. Such defenses ran through Arabia, on the Rhine and Danube, Hadrian's Wall, in Tunisia, South Egypt, etc.
This is typically what we use to denote the Roman borders, but in actuality the limits of the empire were obviously very porous, which is why the Romans relied more on management of immigrants and trade across the borders.
We fill in the bubbles, yes, but there is archaeology that backs up certain "borders" during certain periods - e.g. the distribution of Sommer Type C buckles shows the retreat from the Lower Rhine to the Meuse in the Early 5th Century AD (Swift, "The End of the Western Roman Empire" pages 113-115).
For more in-depth discussion on the concept of Roman "limes" and the frontiers of the empire, check out Isaac, "The Meaning of Limes and Limitanei" in Journal of Roman Studies 78 (125-147) and Kennedy, "Rome's Desert Frontiers" (Routledge, 2012).
