At night's midpoint, bachatzi halielah, is when the Exodus began according to Exodus 12: 29.
Bachatzi halielah has its counterpart in Exodus 12:51; "Be'etzem hayom hazeh," (at the heart of this day - according to some readings), the Lord freed the Israelites from the Land of Egypt. Daylight redemption is the fruit of the process begun bechatzi halielah.
Be'etzem hayom hazeh is about redemption openly triumphing over the doubters and oppressors. Bachatzi halielah is a quieter form, the first steps toward freedom even in darkness.
The sixth-century Israeli liturgical poet Yannai composed a song listing biblical acts of redemption from Abraham's military battles to the victory over Haman and claims that all of them happened bachatzi halielah. Over the centuries, this song has become part of the Haggadah and is sung at the end of the Seder, which is usually around midnight.
The other, perhaps more famous song of bachatzi halielah is the Yehoram Gaon song commemorating a second miraculous rescue from Africa - the 1976 Entebbe raid led by Yonatan Netanyahu. At a time when most people fear to go out and do not have the strength, Israel, is "a nation that will not be still and abandon its children to a stranger".