Trade worked to bring the Roman world together in a number of ways. Trade is something that always tends to bring together people from different areas of the world.
One thing that trade did to bring the Roman world together was to ensure that the Roman Empire maintained trade routes. The empire wanted to be sure that people from its various areas could trade because the trade was economically beneficial. Because of this, the empire maintained a strong navy as well as armies to make sure that trade could happen. The empire also maintained roads, at least in part for trade. Had it not been for trade, the empire would not have been as worried about maintaining these connections and there would have been fewer opportunities for contact between different areas of the empire.
This brings us to the most important way in which trade tied parts of the Roman world together. Trade allowed people from various parts of the empire to come into contact with one another. The Roman world was a tremendously large place. People from Britain and from Egypt, for example, were both part of the Roman world. Trade gave them an opportunity to meet one another. Traders would bring ideas and customs from one part of the Roman world to other parts. When this sort of thing happened, the Roman world became more cohesive since people from its various parts would feel that they understood one another a bit better.
In these ways, trade worked to build connections between areas of the Roman world, thus bringing that world more closely together.