A lawyer asks Jesus how to inherit eternal life, and Jesus affirms that he should observe the two "greatest" commandments - love God and love your neighbor. The lawyer, in an effort to determine the bare minimum he can do to be "saved," asks who he should consider his neighbor.
Jesus responds with a story. It's probably familiar to everyone, but just in case I'll summarize it. A Jewish man is beaten, robbed, and left for dead on the side of the road, and several religious leaders pass him by without helping him. Finally a Samaritan stops, bandages the Jewish man's wounds, takes him to an inn, and pays for his care. After telling this story, Jesus asks, "Who was a neighbor to the beaten man?" The obvious response is the Samaritan - and Jesus tells the lawyer, "Go and do likewise."
First, a historical note. From a Jewish perspective this story would have been shocking. Samaritans and Jews did not get along. At all. There was a significant amount of animosity between the two groups, to the point that they avoided any association with one another.
What is most significant about this parable is that it really does not answer the lawyer's question: "Who is my neighbor?" The lawyer was attempting to limit the circle of people he was responsible to help. Jesus effortlessly correct the question - the appropriate question is not "who is my neighbor?" but "who can I be a neighbor to?" Jesus does so by choosing the most unlikely person to help the man who had been robbed (the Samaritan), after the most likely people (Jewish religious leaders) and already passed him by. Despite the hatred that both men would have felt toward the other, the Samaritan helps someone who by anyone's definition would have been outside the group of people who might be called his "neighbors."
Who, then, is our neighbor? Anyone who is in need. That is the way Jesus answers the question; it is the way we must answer it as well.