It expanded their economy with more items for trade.
It also allowed for language to be decimated...i.e. Vulgar Latin= Spanish, French, Italian, Catalan, Portuguese, Romanian, etc...
Trade also expanded with sheer numbers being expanded.
Roads were built which allowed for travel to be easier.
Ancient Rome was the first civilization to have the idea of Diplomatic Immunity, which is still followed today, strictly might I add.
There are many things that the expansion did for the society and culture. If you want a better list, look up Pax Romana on a legitimate encyclopedia site, not wiki, while wiki is good, it's not a real source.