In a communication to Moses on the 1st of Nissan — two weeks before the Exodus — G‑dinstructed the Children of Israel that "On the tenth of this month, every man shall take a lamb for his family, one lamb for each household... It should be held in safekeeping until the 14th of this month; the entire community of Israel shall then slaughter their sacrifices in the afternoon. They shall take the blood and place it on the two doorposts and on the lintel... They shall eat the meat that night, roasted over fire, with matzahs and bitter herbs..." (this was the first Seder, held on the night the Jews left Egypt). "I will pass through Egypt on that night, and I will kill every firstborn in Egypt, man and beast... The blood will be a sign for you on the houses where you are staying; I will see the blood and pass over you — there will not be any deadly plague among you when I strike the land of Egypt." (Exodus 12:3-13)
The Talmud relates what happened when 600,000 Jewish heads of household began rounding up their lambs on the 10th of Nissan. The lamb was worshipped as a deity in ancient Egypt, so this caused quite a commotion. The firstborn of Egypt, who held the key social and religious positions in Egyptian society, confronted the Jews, and were told: "We are preparing an offering to G‑d. In four days, at the stroke of midnight, G‑d will pass through Egypt in order to execute the tenth and final plague; all firstborn will die, and the people of Israel nation will be freed."
The firstborn, having already witnessed the first nine plagues occur exactly as Moses had warned, approached Pharaoh and his generals and demanded that the Jews be freed immediately. When Pharaoh refused, the firstborn took up arms against Pharaoh's troops, killing many of them. This event is alluded to by the Psalmist, who sings: "[Offer thanks to G‑d,] who smote the Egyptians with their first born” (Psalms 136:10)
Although the date of this occurence was Nissan 10, the event is commemorated not on this date but rather on the Shabbat before Passover (in the year of the Exodus, Nissan 10 was a Shabbat), which is therefore referred to as Shabbat HaGadol, "The Great Shabbat." (This is one of the rare instances in which a commemorative date in the Jewish calendar is set by the day of the week rather than the day of the month.)