The last days of Pesach commemorate the miraculous Splitting of the Sea leading to the rescue of the Jewish People from the hands of their Egyptian pursuers and Pharaoh's last stand against his erstwhile slaves ending in ignominious failure, defeat and powerlessness before the Almighty. The k'riat haTorah for the day is appropriately taken from Parshat B'shalach which recounts precisely this story. The halacha indicates that, unlike its counterpart, Shmini Atzeret, the last day of Sukkot, Sh'vi'i Shel Pesach forms an integral part of the Pesach holiday itself. Hence, whereas the former is a "Regel bifnei 'atzmo" -- an independent festival -- regarding several halachot including the number of korbanot brought, the reciting of the shehecheyanu blessing and the recital of the full Hallel, the latter has none of these characteristics, thus blending in with the rest of the Passover festival.
On a simple plain, the reason for this is obvious. The first day commemorates the initial Exodus, the fifteenth day of Nissan being the day when the Jews left Egypt after the last of the Ten Makkot, the Plague of the Firstborn. The last day commemorates the final step of the Exodus when the pursuing Egyptian forces were destroyed. In the words of Moshe Rabbeinu, "ki asher r'isem es Mitzrayim hayom lo sosifun lirosam 'od 'ad 'olam" -- "for that which you see Egypt (or the Egyptians) today, you will no longer see them forever more!" (B'shalach 14:13).
The Slonimer Rebbe, R. Berzovsky zt"l, in his Nesivos Shalom (Shvi'i Shel Pesach, Ma'amar 4) offers a deeper insight into the connection between the two parts of the chag and the respective events which they commemorate. The first step of the eGGGe'ula was an act of utter Divine rachamim (mercy). Lacking the requisite merit to be redeemed and in imminent danger of becoming utterly assimilated in the Egyptian culture, the Jewish people were rushed out by Hashem (hence, the need for chipazon according to many commentaries). In the language of Yechezkel HaNavi (16:7) cited in the Haggada: "v'at eirom v'eryah" -- "you were unclothed as a newborn," utterly dependent on the mercy of our Heavenly Father. However, such a redemption could not last. A y'shua brought about solely by Divine mercy will eventually cease when Hashem's Attribute of Justice demands that the redeemed deserve their redemption. Hence, Hashem, in his mercy, brought about an event that necessitated K'lal Yisrael's earning precisely the necessary merit to retroactively earn their redemption. This was the episode of K'riat Yam Suf. In the famous words of Hashem to Moshe occasioned by his and B'nei Yisrael's heartfelt prayer for salvation from the rapidly approaching Egyptian hordes, "dabeir 'el B'nei Yisrael v'yisa'u!" -- "tell the Jews they should travel [into the Sea]!" (ibid. 14:15). Rashi comments that Hashem was telling Moshe now is not the time for prayer; now they must travel into the sea. The super-commentaries to Rashi raise the obvious question: is not this time of tsara precisely the time for prayer?! R. Berzovsky's approach answers this question as well. Tefila is a request for rachamim. (Indeed, the G'mara B'rachot (20b) even refers to tefila as "rachamei".) Now, though, such a request would be ineffective. K'lal Yisrael needed the merit of demonstrating their utter faith and trust in G-d by hurling themselves into the Sea even before it split, showing their confidence that no body of water, indeed nothing in the entire universe, can withstand the Power of the Almighty and that in all situations, however bleak, however hopeless, the Go'eil Yisrael can and does deliver salvation. Following the lead of Nachshon ben Aminadav, our ancestors rose to the task and did exactly what was required of them. This mesirus nefesh (wholehearted sacrifice), then, allowed them to earn the prior Ge'ulah. Hence, the events of the last day of Pesach served to solidify and make permanent the events of the first day.
Perhaps we can suggest an alternate approach. The Makkot in Mitzrayim and, indeed, the entire process of the Exodus punctuated by Moshe's coming to Pharaoh demanding the Jews' freedom and Pharaoh's many acts of defiance served a twofold purpose: first, to free the Jews and to demonstrate unquestioningly to them Hashem's Omnipotence and Omnipresence in the world; second, to inform, instruct, and demonstrate to the arrogant Pharaoh who had deified himself and to demonstrate to his nation and through them the entire world that the only true power in the world is G-d himself. Hence, the constant refrain resounds throughout the Makkot: "And you shall know that I am G-d". (See also, "On Makkot and Scientific Endeavors" TorahWeb.org, Pasrahs Bo, 2000) This would also explain why Hashem didn't simply incapacitate all of the Egyptians thus easily allowing the Jews to exit to freedom. To accomplish this second goal of publicizing the Name of G-d to the entire Egyptian people, it was necessary for Pharaoh to bow to G-d's will and to free the Jews. Therefore, it was necessary for Moshe to insist constantly that he release the Jews. He only did this after the last Makka, when he ran through the streets of the capital city, demanding that the Jews leave. However, therein lay a danger. The first goal, to demonstrate Hashem's total mastery over the world to his chosen People necessitated that no other power be involved in the Exodus. Hence, the emphasis, as related in the Haggada that the final Makka was brought about by Hashem bichvodo uv'atzmo: ani v'lo mal'ach, etc. In order to resolve the inherent conflict between these two goals, it would appear that Hashem brought about the ge'ulah in two stages. The first, although orchestrated ultimately by Hashem's power, perforce ended with Pharaoh formally freeing the Jews. The Torah therefore writes "Vay'hi b'shalach Par'o es ha'am," "when Pharaoh freed the Jews" to introduce the Kriat Yam Suf episode. Then, Pharaoh has a change of heart. True, he was forced to consent to free the Jews, but now he reneges on his decision and pursues the Bnei Yisrael to return them to Egypt. G-d then reenters the scene, nullifying Pharaoh's plot and serving as the only source of salvation for the Jews. As a result, the Jewish people would in no way be subservient to Pharaoh for their freedom, only to Hashem himself, and recognize Him alone as the Master of the World and of History. As the Haggada states, "And if Hashem had not taken us out of Mitzrayim, we would have been enslaved to Pharaoh in Mitzrayim." Many commentaries note that the physical slavery might have ended a different way in the course of history, but we would still be enslaved, in the sense of indebtedness, if only Pharaoh had been the one to free us. G-d's intervention at the Sea assured that the B'nei Yisrael were indebted to no other power but Hashem himself.
Only after the drowning of the Egyptians at the Sea does the Torah proclaim: "And they believed in Hashem and Moshe his servant." Only then do B'nei Yisrael sing to Hashem as their only source of our salvation: "Hashem Ish Milchama" and "Ozi v'zimras kah, va'yhi li lishua!" What was explicit at the time of the original Exodus and will again be apparent at the time of the ultimate Redemption (see "Parallels between the Exodus from Egypt and the Final Redemption" TorahWeb.org, Shabbos HaGadol, 2002 ) is true throughout history. Although Hashem's hand is often hidden, and He works through many agents, He is always the One solely arranging the events behind the scene. May we merit always seeing the Guiding Hand of Hashem in our private lives and the events affecting Klal Yisrael.