HaAzinu marks the final time in the Torah where Hashem foretells the future generations of Klal Yisroel after they enter Eretz Yisroel. Indeed, some M’phorshim understand that HaAzinu contains detailed allusions to everything that will happen to the Jewish people. After predicting that there would be many years of peace and plenty, the Torah warns that B’nei Yisroel will become “fat”. (HaAzinu 32:15) Inevitably, we would then enjoy our blessings and forget from where they come. Hashem then describes the calamities which would befall us as a result of our transgressions. (32:22-26). Curiously, the Torah then tells us that Hashem will temper his wrath, so that our enemies do not question the existence and presence of Hashem. (32:27)
This same concept was advanced twice before in the Midbar, both times by Moshe Rabbeinu. The first was after the Cheit Haegel, where Moshe pleaded, why should the Mitzrim be able to claim that you took them out just to kill them in the mountains? (Shemos, 32:11-12) And again after the Meraglim, where Moshe warned that the nations would claim that “Hashem was unable to bring Bnei Yisroel into the land…so he killed them in the dessert” (Shelach, 14:14-15) Three times we are spared Hashem’s full wrath so that the Goyim would not question Hashem’s sovereignty. Why does Hashem care what the Goyim think, or even us for that matter?
The Zohar points out that Hashem created the World so that people could perceive and appreciate His greatness. (Zohar, II: 42b) After establishing His Bris with Bnei Yisroel, it became incumbent upon us to illuminate for the goyim Hashem’s greatness. We are the chosen people. The goyim look to us for their understanding and perception of Hashem. When we fulfill the Mitzvos, we receive disproportionate Bracha and the Goyim see that Hashem rewards us for following in his ways. Conversely, when we stumble and suffer, the goyim simply see no divine providence in the world whatsoever. That is the meaning of the next Pasuk. They are without good counsel, they simply do not understand (HaAzinu 32:28).
That is in essence what is meant by our being an Ohr Lagoyim. (Yishaya 49:6
and 60:3). We are the conduit through which the world views Hashem. When we live our lives according to the Mitzvos, the goyim perceive Hashem’s presence and when we stray they see no illumination whatsoever. As we strive to reach our highest levels during the Yomim Naarayim, we must make this one of our goals. And even afterward, when there is often an inevitable decline from the heights we try to achieve, we can enlighten the world even in the mundane. Being compassionate and caring for people, being honest in our professions, being pious of our role – these are all ways that we can make every day productive in fulfilling our part of the Bris. By following Hashem’s ways when we learn Torah, fulfill the Mitzvos and take this code of behavior into the world with us, we are allowing the goyim to perceive Hashem’s greatness and at the same time insuring his mercy when we fail. Hashem does care what the Goyim think and it is our job to allow them to see his greatness
 There are several other “reasons” posited for why Hashem created the World from a multitude of great sources including the Gemara, the Rambam and the Ramban, but the Zohar’s discussion seems most relevant to the present discussion.