Why does the Torah spell "Yadchah" with a 'Hei'?
Moshav Zekenim: The superfluous Hei hints that Tefilin is worn on the upper arm, above five joints (three in the fingers, and the wrist the elbow).
Hadar Zekenim: If his right hand is weaker, he puts on that hand.
Rosh: Totafos hints to four in the head Tefilin. Moshav Zekenim - we learn the number of walls of a Sukah from the three times that "ba'Sukos" is written. Why don't we learn 12 boxes from the three times that 'Totafos' is written? It is because they are not written in one place.
Moshav Zekenim citing ha'Chasid: Why didn't the Torah explicitly teach four boxes for the head Tefilin? This teaches that they should be from one piece of hide.
What exactly, does "Totafos" mean?
Rashi #1: It is the acronym of 'Tat' and 'Pas', the former being the Caspi word for two, the latter, the African word, due to the four Parshiyos 1 that comprise the Tefilin shel Rosh.
Rashi #2 (citing Menachem ben S'ruk) and Ramban: It is a Lashon of speech, 2 and is similar to the Lashon "Zikaron" mentioned in the first Parshah of the Shema, inasmuch as people who see the Tefilin shel Rosh 'bound between the eyes' will remember the miracle and talk about it.
Ramban: It is named after Totefes 3 - the name of an ornament that women wear on the forehead from ear to ear.
Targum Onkelos and Targum Yonasan: "Totafos" is synonymous with 'Tefilin'.
Why is it important to remember Yetzi'as Egypt?
Ramban #1: Because Hashem declines to perform miracles for the Rasha'im and deniers in every generation (like He did for Pharaoh). Therefore, He strictly 1 commanded us to remember the miracles of Egypt in all different ways (including wearing it on arms and head, fixing it on our doorposts and mentioning it daily with our lips - as a constant reminder, never to be forgotten. 2
Even to the point of sometimes punishing with Kares (like we find by Chametz and the Korban Pesach).
Moreover, remembering the miracles of Yetzi'as Egypt forms the basics of Emunah (Refer to 8:18:1:1**). See Ramban, who elaborates at great length on this issue.
Because a person who believes that nature takes its own course (and is not the manifestation of Hashem's will) does not have a portion in the Torah (See Ramban, DH 'U'min ha'Nisim ha'Gedolim').
Which is particularly relevant, bearing in mind that nobody was around when Hashem created the world, whereas all of Yisrael witnessed the miracles in Egypt (Ramban).
Note; we also find the corollary between Yetzi'as Egypt and Ma'aseh Bereishis by Shabbos, where we refer to the former in Kidush in the evening, and the latter, in Kidush in the morning.