This Shabbos, the Shabbos preceding Pesach, is known as Shabbos Hagadol. There are several reasons for this.
Tosafos, in Shabbos 87b (d”h “ve’oso”) says the Shabbos is called great because a great miracle occurred on that day when the Jews were in Mitzrayim. According to the Midrash Rabbah on Parshas Bo (cited by Tosafos): On that Shabbos, when the Jews took lambs for their korbanos Pesachim, the firstborn Mitzriyim asked them what they were doing and why. The Jews responded that they were going to slaughter the lambs as sacrifices to Hashem so the firstborn Mitzriyim would die. The firstborn Mitzriyim then pleaded to their fathers and Pharaoh to set the Jews free. When the request was denied, the firstborn waged war and killed many of their fellow Mitzriyim. This is the meaning of the pasuk we recite in Hallel gadol: “lemakeh Mitzrayim b’bechoreihem ki l’olam chasdo.”
The Maharshal suggests that Shabbos Hagadol got its name from its Haftarah, which includes a pasuk that refers to a day in the future that will be “gadol.” We anticipate this day, and therefore named the Shabbos after it.
The Kli Chemda quotes the Gaon Rav Yisroel Nasson, who suggests an explanation for the name Shabbos Hagadol but first states that his p’shat is only “b’derech tzachus” (a humorous parody).
He begins with the following midrash: While Moshe Rabbeinu was still living in Pharaoh’s palace he managed to convince Pharaoh that the Jews should have one day off each week – Shabbos. The Tur (281) says this midrash explains the tefillah we recite in the Shabbos Shemoneh Esrei l’Shacharis: “yismach Moshe b’matnas chelko” – Moshe should rejoice with his lot. It refers to Moshe picking the day that Hashem ultimately chose as the day of rest: Shabbos.
Based on this midrash, Rav Yisroel Nasson suggests the following. When Bnei Yisrael were in Mitzrayim they were considered Bnei Noach. Although they kept certain mitzvos, they only did so as a stringency. One difference between Bnei Yisrael and Bnei Noach is that shiurim only apply to Bnei Yisrael. For example, only Bnei Yisrael are liable for eating a k’zayis worth of forbidden food while Bnei Noach are liable for eating any amount. Several Acharonim opine that since the age when one becomes bar mitzvah is also a shuir, it too only applies to Bnei Yisrael. Bnei Noach, on the other hand, are liable for their actions as soon as they become aware of what they are doing. Thus, in Mitzrayim, Bnei Yisrael were responsible for their actions before age 13.
But this changed on the Shabbos before they left Mitzrayim, for then they were commanded to fulfill the mitzvah of korban Pesach, and we know that no non-Jew may sacrifice a korban Pesach. Hence, the Jews’ status must have changed from Bnei Noach to Bnei Yisrael. If so, this was the Shabbos when Bnei Yisrael became responsible for their actions only after the age of 13. The Shabbos became known as Shabbos Hagadol, therefore, because it was on this Shabbos that only gedolim were responsible for their actions.
Not all Acharonim agree, however, that Bnei Noach are responsible for their actions before 13. The Kiryas Sefer differentiates between two types of shiurim. One type is a measurement of how much of a certain thing is required, i.e. a k’zayis or a prutah. If one eats a half k’zayis of pig he has eaten pig. He will not receive lashes because he did not eat a sufficient amount – but he has still eaten pig.
There is another type of shiur – an amount that creates a new entity or situation. Less than this shuir means “nothing” has happened. An example of this is techum Shabbos. The shuir of techum Shabbos is 2,000 amos. If one walks 1,000 amos out of the city, he has not violated half the prohibition. He has done nothing wrong. Until one walks the entire shiur of 2,000 amos there is no techum involved whatsoever.