Rabbi Levi Yitzchak Schneerson, the father of the Lubavitcher Rebbe (Likkutei Sichot, volume 21, p. 71) explains that "so that you may remember the day of your departure from the land of Egypt as long as you live" (Devarim 16:3)- is to teach us to remember that we are out of exile, we have left Mitzrayim, we have left the bondage of Pharaoh.
The Gemara (Berachos 14b) is teaching us something similair, however in a different context:
Who took us out from Egypt and redeemed us from the house of bondage
The Alter Rebbe (beginning of chapter 47 of Tanya, Likkutei Amarim) teaches us that the teaching of both the Gemara and Mishnah (Pesachim 116b and 10:5-6), that in every generation, a person must view himself as though he personally left Egypt, means that you must remember that the divine soul was released from the "serpent's skin"- the bondage:
"In every generation and every day a person is obliged to regard himself as if he had that day come out of Egypt." This refers to the release of the divine soul from the confinement of the body, the "serpent's skin," in order to be absorbed into the Unity of the light of the blessed En Sof, through occupation in the Torah and commandments in general, and in particular through accepting the Kingdom of Heaven during the recital of the Shema, wherein the person explicitly accepts and draws over himself His blessed Unity, when he says: "The Lord is our G‑d, the Lord is One."
See also Maamar Kimei Tzeischa Mei'eretz Mitzrayim - Part II from the Lubavitcher Rebeb:
The daily remembrance of the exodus from Egypt focuses primarily on one dimension of exodus, departing from the straits of unholiness; it highlights the exodus from the limitations that hinder Torah study and impede the performance of the mitzvos.
@DanF in his comment states "I think the main thing is to be aware that Yetziat Mitrayim was done as a necessary perquisite to coming to Har Sinai and receiving the Torah, which in turn, obligated us and defined the list of mitzvot". According to the Rebbe, this is true. The Rebbe explains that the rememberance of the Exodus highlights the exodus from the limitations that hinder Torah study and impede the performance of the mitzvos.
However, according to Rabbi Eliezer Melamed in his Peninei Halakhah (Pesach 15:2), the mitzvah of "remembering the exodus" can be fullfilled by praying Shema twice a day:
To fulfill the obligation to invoke the Exodus every day and night, we recite the third paragraph of Shema each morning and evening, as this paragraph states: “I am the L-rd your G-d Who has taken you out of Egypt to be your G-d: I am the L-rd your G-d” (Bamidbar 15:41).