The Shabbat preceding the Passover festival is called the Great Shabbat in commemoration of the great miracle that occurred on the Shabbat preceding the exodus from Egypt. It is based on the tradition that when God ordered the people of Israel to prepare a lamb on the tenth of Nissan for the paschal offering, the Egyptians were paralyzed with fear and could not prevent the offering of the Egyptian deity, the lamb.
Another explanation of the name is from the Haftarah which ends with the words: "Behold, I will send you Elijah the prophet before the great and awesome day of the Lord. He will turn the hearts of fathers to their children and the hearts of children to their fathers." (Malachi 4:5-6)