There is this saying that Rome conquered the world in self-defence. That is obviously not true but it speaks to the mindset of the romans at the time.

Before the first punic war, there was the Phyrric War (280-275BC). This was a big wakeup call tot he Romans, as their territory was invaded by a foreign nation (not Gauls or other barbarians). After that, Rome became much more conscience about their state security.

But I think that the gobbling up of territory really got going with the punic wars. Rome was actually faced with the possibility of being destroyed (or at least defeated) by another nation and Hannibal shook the Romans to their very core. Not for 500 years would they face such danger. So as they defeated Carthage over the next years they took lands that used to be controlled by Carthage either as provinces or client. Iberia, modern day Spain, North Africa, the mediterranean islands for example.

But during the second punic war, other regions entered the conflict as well. Macedonia allied with Hannibal and therefore made an enemy of Rome. Obviously they bet on the wrong horse there. They would make clients out of many of the greek territories, outright annex others at later parts. So within like 5 generations Rome grew from this middle italian city state really into a state that spanned from Spain to the Bosporus. In the roman eyes, this was needed to keep the state secure by elimating potential enemies.

Obviously there is a whole nother factor in this: Conquest brings in lots of money. Slaves, Loot, new farmland etc. The riches that were acquired in these conquest must have been massive. And of course this would incite roman politicians to further pursue war with, to get their share of the pie that is Conquest. At least up until the Principat of Augustus, Conquest was used as a means to acquire personal wealth and prestige. Pompey the Great was so powerful because of his campaigns in the east, bringing in not only money but huge amounts of clients. Marcus Crassus basically declared war against Parthia in the east for personal Glory. Ceasar escalated the situation in Gaul for very similar reason. In the late republic expanding Romes border was a means of political advancement in their oligarchical system.

Later in the days of the Empire, the massive Expansion couldn't really be maintained as it was in the middle and alte republic. So when they did it was often to secure their border. The Rhine river, the Carpathian Mountains, Arabia etc. Roman expansion basically stops in the 2nd century after Emperor Trajan. In 117 ad Rome has reached its peak (territoriy wise)

There are so many more aspects and I can't do them justice at all. But i think the roman expansion really kickstarted in the post punic war era politics.

Some literature that you might find useful for your question:

-William V. Harris: War and Imperialism in Republican Rome

-E. Badian: Roman Imperialism in the Late Republic

-Sherwin-White: ‘Rome the Aggressor?’ In: The Journal of Roman Studies, Vol. 70

I hope this was at least somewhat helpful.