The Uraeus (plural Uraei or Uraeuses; from the Greek οὐραῖος, ouraîos, "on its tail"; from Egyptian (iaret), "rearing cobra") is the stylized, upright form of an Egyptian cobra, used as a symbol of sovereignty, royalty, deity and divine authority in ancient Egypt.
Certainly Moshe and Aharon saw Pharaoh wearing the Uraeus in his court and no doubt all of Egypt, including the Children of Israel knew what the symbol meant. In Western culture we don't expect to see royalty wearing "a snake-like crown," yet in some parts of the world "head-dresses" are a common occurrence:
In India the maangtika is a traditional head piece worn most often at weddings, traditionally by the Hindu bride. It consists of a metallic string, with an attractive pendant attached at one end, which may be of any shape and adorned with precious or semi-precious stones. The maangtika is worn at the middle parting of the hair. Muslim brides wear a jhoomar, which is a similar beautiful ornamental head piece, on one side of the forehead.
Bajuband and Vanki are traditional armlets worn on the upper arm. They often have to be secured in place with a gold string. Armlets were traditionally worn by Indian men and women. Some common designs on them include creepers or snakes entwining.
While these Egyptian and Indian customs symbolize different things their relevance to the meaning of tefillin should be apparent even though these customs do not explain the usage of the words totafoth (tefillin shel yad and shel rosh) or totafeth (appuzainu, an ornament worn on the forehead.") in the Torah and the Mishnayoth.
For a discussion of the term totafoth see this article http://www.balashon.com/2007/01/totafot.html where
Tigay also suggests "headband", but derives the word totafot from the Arabic tafa - "go around, encircle".
Tigay discusses the derivation in this article here: On the Meaning of T(W)TPT on JSTOR.
Rashi on Shmoth (13:16) says the totafoth are to be worn as "an ornament" between the eyes; although the Torah (Shmoth 13:9) refers to the totafoth as a zikkaron (remembrance - memorial) for whoever sees them [the tefillin] bound between the eyes will recall Pesach and the miracle [of the Exodus] and speak about it, as it says, "that the Law of HaShem may be in your mouth" (13.9).
When we say a Bracha over the Hand tefillin we say it with the intention that the Bracha covers the Head tefillin as well. It is explained that the single bracha covers both because, it says, "bind them for a sign upon your arm and let them be for a remembrance between your eyes;" and them is written in the plural (them being the words of Torah).
We read in Shmoth 33.4-6 "And when the people heard these evil tidings, they mourned; and no man did put on him his עֶדְיוֹ ornaments. And the L-RD said unto Moses: 'Say unto the children of Israel: Ye are a stiffnecked people; if I go up into the midst of thee for one moment, I shall consume thee; therefore now put off thy ornaments עֶדְיְךָ from thee, that I may know what to do unto thee.' And the children of Israel stripped themselves of their ornaments אֶת-עֶדְיָם from mount Horeb onward."
The Hebrew root used for ornaments is ayd (witness): Maimonides writes in his Mishnah Torah (4.26) that "one who prays the Shema without wearing Tefillin violates eight precepts of the Torah and bears false witness against himself!"
Isaiah 43.10 states "Ye are My witnesses, saith the L-RD, ...."
Thus, we see from non-Jewish cultural traditions or customs and from Jewish custom that the totafoth (ornaments) serve as a symbol of sovereignty, authority, and royalty; and should be for Jews as a constant reminder of Pesach, of the Exodus and that the Jew is always a witness of HaShem's miracles; which, upon seeing the totafoth worn on the forehead would elicit or inspire a discussion of HaShem's Oath to the Patriarchs and of HaShem's as well as Israel's sovereignty, authority, royalty and the miracles leading up to the sanctification of the firstborn, the Passover Festival, the Exodus and the conquest of and settlement of Canaan (Eretz Yisrael).