what led to the expansion of Rome was it's increase in population which meant it needed more food and the promise that everyone who survived 25 years of service in the roman legion or army get 3 acre of land so if you need food then they have to get more land to farm and feed Rome and you need more people to grant people land which meant more conquering and the cycle repeat
the roman empire expanded through wars with it's neighbors and conquering them and taking their land as their own and it expanded pretty big the they captured all of the area surrounding the Mediterranean
some of it's lasting effect it give birth to the republic which is like democracy and the idea of senate whch we use up to this day
hope it helped