A night filled with excessive drinking to the point that events of the said night are hazy and cannot be completely recalled. There are varying degrees of "doozy", the most common being a night filled with drunken hilarity that for the most part is only recalled by those who did not get too drunk, or partake in the "doozy". A person who has a doozy usually wakes up the next morning wondering where he/she is, often times confused about the events of the night before.
"man...last night was a doozy."
"Remember last New Years? Me neither, it sure was a doozy."