To put it simply-the Romans were very smart.
To begin with, they had a brilliant and powerful army. They did not always storm in and create mass chaos. They could negotiate. If they wanted to take over a particular area, they could offer protection to that area. There were many other civilizations during this time that were not very civilized so it was better to let Rome conquer peacefully and have their protection at the same time.
Rome was also ahead of it's time. They took concepts from other civilizations and used them to their advantage. They were very advanced for the age.
In addition, Rome was technologically advanced in both its daily life and in its military, so much so that there were few militaries on Earth that could resist them for long, at least as the empire was in its ascension. Think of the US military now and the technology it uses, compared to most other militaries, and Rome had similar advantages.
Diplomatically, they were very sharp in how they dealt with other countries, as they took over vast territories even without war as nations and peoples realized it was better to be subservient to Rome than to be destroyed by them. In many cases, being part of the empire brought more benefits than disadvantages, so there was an incentive to submit. Think of how Puerto Rico is part of the US empire still, but does not want to become a state, nor declare independence, even though their culture and language are very different from most of the US. There are benefits for them to be a part of the US without resistance. Not the same, but the analogy works.
Rome was able to conquer such a large empire partly because of the superb discipline and organization of its armies. It was able to rule the empire because it set up a system of government that allowed people from the various conquered regions to rule themselves, mostly, with just a little oversight from the Romans.
Most of the people the Romans conquered were much less used to fighting in disciplined units and using organized tactics. Roman armies were too strong for such opponents.
When the Romans conquered an area, they usually left its elites in place and just put a Roman governor in over them. That way, the "natives" still had a lot of control and were less likely to rebel.
I would say three main reasons:
1. Technology, they borrowed from other cultures and were inventive themselves regarding infrastructure and military.
2. Required military service and well trained soldiers and generals.
3. Just like today, prosperity. The peace they offered in the region caused the economy to flourish and that rising tide lifted all ships. It paid to be a Roman citizen!