The Siduro Shel Shabbos (Chelek 2, Hadrush Harishon) explains this with a moshol of a king who knows that someone has a serious complaint against his son that he wants to bring before him. The king knows that he must listen to every complaint, even if it is against his own, beloved child, but he also doesn't want to be placed into a situation where he may have to punish him.
The wise king comes up with a plan. He told his guards that when the complainant arrived, they should start singing and dancing with him. They should make him so happy that he would forget his complaint and leave.
The nimshol is that when Hashem wanted to take our ancestors out of Egypt, He knew that there would be a complaint that the nation was unworthy. These complaints actually were made at the Yam Suf, but by that time the nation possessed the merit of believing and trusting in Hashem and following Him into the wasteland, and that merit was able to silence the complaint. At this time, however, they were still on a lowly level and possessed no merits.
So what did Hashem do? He suddenly shone a great light of holiness onto the world and the Upper Worlds that caused the complainants to close their mouths and leave.
This explains the use of the term "chozek yad" (strong hand) that is used to describe how Hashem took us out of Mitzrayim. In a display of strength, Hashem sent a tremendous amount of light to the world in order to silence the complaints. We repeat these words numerous times as we praise Hashem during the Seder, in order to express our gratitude for saving Klal Yisroel in such a mighty and supernatural way.