Rome is a port city that has easy access to the ocean as well as the surrounding mountains. By nature of a series of treaties, it was able to effectively protect itself from invaders. Also, its location on the Italian peninsula made both Africa and Europe easily accessible.
Rome was not only able to establish a military stronghold within the parameters of its borders but also founded solid trade relationships with surrounding countries that made the import and export of goods and supplies convenient and fast. Having a heavy sea presence also meant that Rome could exercise control over much of the surrounding areas. Once Rome was able to expand its army, it could send troops both north on land and south via the sea. Most other established civilizations of the time did not have the benefit of both foot soldiers and sailors.
Rome was also located within an area in which multiple city-states existed, which simplified communication with surrounding societies, in particular those with which it was necessary to form alliances. Taking over opposing city-states was also simplified as a result of close geographical association. As Rome spread, so did its army, which made it easier to organize more troops and continue to expand.