First of all, I didn’t make up this description. The source for being “a light unto the nations” is from the prophet Isaiah, chapter 42, verse 6. Isaiah was relaying the word of God, and described the role of the Jewish nation as such.
What does this mean? That we are better than other nations? Not really. It means that we were given a special responsibility to share our tradition and experience in the beliefs and practice of ethical Monotheism with all other nations of the world. This is the “light” we are responsible to “shine”.
Although we have the responsibility as a national unit to be a “light unto the nations”, this requires us as individuals to reach upwards towards God. This means that each and every one of us has to work hard to retain a sense of our spiritual persona in order to be able to turn ourselves into role models for those around us. How does one go about doing this? Primarily, by improving our interpersonal relationships; making sure that we are kinder, more thoughtful and gentler people. If we can succeed at doing that then we will truly become a light unto the nations. It is a position of great responsibility, but the global and spiritual rewards are commensurate to the responsibility.
By the way, here is another (famous) quotation: “The Jew is that sacred being who has brought down from Heaven the everlasting fire, and has illumined with it the entire world. He is the religious source, spring, and fountain out of which all the rest of the peoples have drawn their beliefs.” Who wrote this? None other than Leo Tolstoy.