The seventh day of Passover is not a separate Festival in its own right, as is the case with Shemini Atzeret, the last day of Sukkot. Rather, it is the conclusion of Passover and we therefore do not recite the Shehecheyanu blessing when making Kiddush or lighting candles.
The seventh day of Passover marks the day when many miracles were performed for our forefathers at the Red Sea. The Torah (Exodus, 2:15) states: And the seventh day shall be declared a holy day for you. No work shall be done on that day.
In most of the instances where the Torah refers to the first day of Passover, mention is made of the Exodus from Egypt. Regarding the command to observe the seventh day of Passover, however, no mention is made of the miracle of the splitting of the sea which took place on that day. Moreover, when the Torah refers to the miracle no mention is made of the date on which the miracle took place.
Holidays were not given to Israel to mark the downfall of her enemies. Rather, they were ordained to commemorate Israel's salvation. The Holy One, blessed is He, does not rejoice when the wicked are destroyed, and Israel is also not to celebrate these instances. Israel was commanded to observe the last day of Passover even before she knew that the Egyptians were destined drown in the sea on this day. The Torah therefore ignores the link between the last Festival day and the splitting of the sea.
The essence of the celebration of this day is the song that Moses and Israel were Divinely inspired to sing on this day a song that merited being included in the Torah, a song to which G-d and His heavenly consorts listened.
Although the Torah saw fit not to mention that the drowning of the Egyptians took place on this day for the reason that we have already mentioned, we have a tradition that this event took place on this day. Once it was permitted to commit the oral tradition to writing, we have written sources for this as well.