We say in the shemonei esrei on Rosh Hashanah:

“All who has a soul in his body will say, Hashem the G-d of Israel is King, and His kingship extends through all of creation.”

The question is asked “Why is it so important that even the Gentiles coronate Hashem?”

The Medrash (Parshas Eikev) tells us that when one friend praises another friend, it is not very dramatic because one friend will typically overlook the negative aspects of the other. However, when a person’s enemy praises him, it is truly an astounding event because it shows he has won the enemy over, from being antagonists to becoming well-wishers. With this we understand that which Dovid HaMelech writes in Tehillim (117) “Shabchuhu kol ha’umim” – all the nations praise you. At the time of the Exodus, Hashem used acts that were so wondrous that the other nations of the world – though they naturally despised the Jews – stood in awe and admired them. At the time when Moshiach will come and all the falsities will be unmasked, the gentiles will again stand in awe of Hashem. However, this could be accomplished without us. Therefore, our prayer on Rosh Hashanah is for Hashem to attain this recognition by placing us again on a pedestal, by inter-relating with us in a way that shows that we are His nation, His servants, and we have this special relationship with Him of “avinu malkeinu” – our father, our master.

This extends into the 10 days of repentance, as we continue to daven that we want Hashem’s presence to be felt. The words of the shemoneh esrei Elokei Yisrael melech” are a plea that we should be the vehicle through which Hashem’s majesty is expressed in the world. How do we accomplish this? What does this require us to do? In shemoneh esrei we plead to Hashem “l’maancha elokim chaim…”: We ask Hashem to give us life, but with context and purpose to bring about the glory of Hashem. By stating that we want success for Hashem’s sake binds our success to His apparent success. This is what the opening phrase means: Hashem should be viewed as our King, and then His kingdom will spread over the rest of the world. With us or without us, Hashem’s superiority will be achieved. Our goal at this time is to become a worthy servant, looking only to do His will, so that His benevolence be bestowed on us in a wondrous way. Through this, we will become a source of a Kiddush Hashem, bringing about the ultimate glory of Hashem, showing that He rules the world. (adapted from the Vilkmayer Maggid)