The Tur (O.C. 430) writes that the reason that the Shabbos that precedes Pesach is referred to as Shabbos HaGadol is because of the miracle that occurred to the Jewish People. The year that the Jewish People left Egypt, the tenth of Nissan occurred on Shabbos, and every Jew tied the sheep that they were going to sacrifice for the Korban Pesach to the foot of their bed. When the Egyptians questioned the Jews regarding this strange behavior, the Jews responded that they would be sacrificing the sheep for HaShem. The Egyptians were irritated but they could not respond. The Bais Yosef quotes Tosfos who writes that the Medrash states that when the Jewish People took their sheep for the Korban Pesach, the firstborns of the Egyptians questioned them and the Jews responded that they would be sacrificing the sheep to HaShem, Who would subsequently slaughter all the Egyptian firstborn. The Egyptian firstborns requested from their fathers and from Pharaoh that he allow the Jews to leave Egypt, and Pharaoh refused. The firstborns then waged a battle and many of them were killed, and this is the meaning of the verse (Tehillim 136:10) lemakei Mitzrayim bivchoreihem, to Him Who smote Egypt through their firstborn. The Belzer Rebbe, Reb Yissachar Dov zt”l asks, we can understand according to the Tur that the miracle was that the Egyptians did not kill the Jews, despite the fact that the Jews were slaughtering the Egyptian gods. According to the Medrash quoted by Tosfos, however, it is difficult to understand what the miracle was for the Jewish People. Reb Yissachar Dov answers by quoting his father who said in the name of Reb Dov Ber that it is said (Shemos 2:23) during those many days, it happened that the king of Egypt died, and the Children of Israel groaned because of the work and they cried out. Their outcry because of their work went up to G-d. As long as the gentiles dominate the Jewish People, the prayers of the Jews cannot ascend to heaven. Thus, when the king of Egypt died, only then were the cries of the Jewish People capable of ascending heavenward. According to this explanation, says Reb Yissachar Dov, we can understand the Medrash that Tosfos quotes. When the firstborns killed many Egyptians, this was the beginning of their downfall, and this was the miracle for the Jewish People. It is specifically for this reason that this Shabbos is referred to as Shabbos HaGadol. Alternatively, it is the nature of a father to have compassion on a son, and the Egyptians should have had compassion on their children that they should not die. Thus, the Egyptians should have freed the Jewish People prior to the plague of the death of the firstborn. Had the Jewish People left with permission from the Egyptians, the Jewish People would have retained some form of gratitude towards the Egyptians, and the Exodus would have only been in a physical manifestation. HaShem desired that the Jewish People be freed physically and spiritually, i.e. that no contamination from the Egyptians remain by the Jewish People. Furthermore, HaShem desired that in the merit of the great revelation, the Jewish People would be prepared to receive the Torah. For this reason HaShem demonstrated to the Jewish People that the Egyptians were still rebellious and their hearts were hardened, which did not allow the Egyptians to let the Jewish People go free. In this manner the contamination of the Egyptians was completely uprooted from within the Jewish People, and this was a great miracle for the Jewish People. For this reason this Shabbos is referred to as Shabbos HaGadol.