The most common explanation is given by Rashi and by many other halachic sources. "This is because in Nissan (this month), Bnei Yisrael (Children of Israel)left Egypt on Thursday, which means that they set aside the lamb for the sacrifice on Shabbat, the tenth of the month. Bnei Yisrael asked, 'How can we sacrifice the abomination of Egypt before their very eyes and they will not stone us?' [Shemot -Exodus - 8:22]. The Almighty replied, now you will see the miracle. And since miracles were performed for them on that Shabbat before Pesach, it was given the name Shabbat Hagadol."
Thus, the main significance of Shabbat Hagadol is an atmosphere of freedom for Bnei Yisrael (the children of Israel). They no longer feared the Egyptian masters, and this led to the possibility that "this month is the beginning of the months for you" [Exodus 12:2]. Not only were they free from the Egyptian taskmasters, they now had their own calendar. They were no longer bound to the idol worship of the "beautiful calf, Egypt" [Jeremiah 46:20], this abomination was to be forgotten! However, it was not sufficient for the nation just to eradicate idol worship, it was necessary to provide the nation with its own type of holy service. "Turn away from evil" is a good practice, but it must be accompanied by "do good" [Psalm 34:15]. The Torah portion for this week, includes positive action, with the high point being the receipt of the Torah at Sinai. The essential element of the Olah sacrifice that Bnei Yisrael was commanded to bring is not the sacrifice itself but rather the dedication and self-sacrifice. Bringing a sacrifice is an act that symbolizes offering the soul for the good of the Torah. While it is true that the Olah is burned completely on the Altar, the main requirement is that "the flame on the Altar shall burn within HIM" [Deuteronomy 6:5], referring to the person who brings the sacrifice. The Olah can teach a man to dedicate all his actions to the Almighty, with nothing left out. Samuel tells us, "to obey is better than a sacrifice, to listen is better than the fat of rams" [I Samuel 15:22]. If a sacrifice does not symbolize good deeds it is meaningless. This duality, eradicating the bad while maintaining the good, is what leads to the message in this week's Haftara: "Behold, I send the prophet Eliyahu to you, before the great and awesome day arrives" [Malachi 3:23].