This Shabbat is known as Shabbat Hagadol, the Great Shabbat. There are numerous reasons found in Chazal for the choice of this name. Some say the reason is because the word Hagadol appears in the special Haftara that was designated to be read this Shabbat.
The Mishna Berura offers another reason. He writes that when Bnai Yisrael were in Egypt they were commanded to take the שה, sheep, which was the god of the Egyptians, on tenth of Nissan, which was a Shabbat that year, parade it through the streets of Egypt, and tie it to their bedposts so they could examine it for four days to make sure it was perfect for slaughter on the 14th of Nissan as a Korban. Because of this great miracle, that that the Jewish People did this and were not afraid of the Egyptians on that Shabbat, the Shabbat prior to Pesach received the name Shabbat Hagadol.
Rav Moshe Feinstein, in his Darash Moshe, offers another reason. He explains that Shabbat testifies that Hashem created the world יש מאין, from nothing. The holiday of Pesach teaches us that Hashem continues to run the world. There are some people who believe that Hashem runs the world, but they do not believe that Hashem created the world. Such a person is considered a מין, heretic, and one who denies the existence of Hashem. Without the belief that Hashem created the world, one must think that there is another power in this world, because even if he believes that Hashem is the Leader of the world, he still thinks there is something He could not accomplish. This was the mistake of Paroh. He believed that the plagues were from Hashem and that Hashem runs the world, but since he did not believe that Hashem created this world he thought that he could find a weakness of Hashem. Therefore, before we celebrate the holiday of Pesach that illustrates that Hashem runs the world and took a nation from the midst of another nation, we must celebrate this Shabbat, which commemorates that Hashem created the world and it is the same Hashem Who accomplished both feats. This is also why the Torah lists the order of the Yamim Tovim beginning with Shabbat; without our proper belief in Shabbat the keeping of Yom Tov would be useless. So Shabbat is called Hagadol, great, since we require this message of Shabbat to truly appreciate the message of the Yom Tov of Pesach.
The Gemara in Masechet Rosh Hashanah (11a) quotes Rabbi Yehoshua, who says that in the month of Nissan we were redeemed from Egypt and the future redemption will also take place in Nissan. May we learn from this message of the connection between Shabbat and Pesach well; let us strengthen our belief and commitment to Hashem and His Torah, and let us hope that this Nissan is the Nissan that the Gemara referred to, when we will be able to sing a Shir Chadash, a new song of praise, to Hashem.
Tosafot in Pesachim (127b) quotes the Mechilta, which says that all the other songs are called in feminine (Shira) except for the song we will sing when Mashiach arrives, which will be called in masculine (Shir). Why? The explanation is that a woman has the pain of childbirth. The other miracles involved pain as well. But when Mashiach comes, there will not be any more pain. May Hashem say that we have had enough pain so we can sing this Shir Chadash and so that His great Name should be one and accepted by everyone.