The stories behind the beginning of a civilization or culture play a big part in shaping the way the culture views itself, whether they are true or not. For example, the George Washington cherry tree story teaches Americans that our first president (and therefore, theoretically all those that followed) was an honest man that could not tell a lie.
The same thing is true in the legends surrounding the founding of the city of Rome. The Ancient Romans believed their great city was founded in violence, blood, and victory. That tale is told in the story of Romulus and Remus.
According to the legend, when the boys grew up they decided to found a new city where they had been rescued by the she-wolf. There was a disagreement as to exactly where to build the city, and Romulus killed Remus. The city Romulus built was named Rome in his honor.
What effects does a legend like this have on the people it is meant for?
The Romans were not very tolerant of dissension or disloyalty. This is certainly part of the myth. The myth also quite explicitly claims that Romans were descendants of a god (Mars). Therefore they could not be beaten in battle (or so they thought), and their rulers' orders could not be questioned. Basically it gave the Romans a reason to believe they were better than everyone else.