The gemara explains that this announcement was made on Shabbat, and part of its purpose was to warn people not to carry the objects for the Mishkan from their private domains to the central encampment via the public thoroughfare. And it is from this verse that we learn that carrying from one domain to another on Shabbat is a forbidden melacha. (Shabbat 96b.)
The labor of moving an object from one domain to another, seems like the most insignificant of all the melachot. Indeed, some early commentators call it an "inferior labor" (Tosafot Shabbat 2a). After all, nothing is really done to the object - it merely changes location. (See Beur Halakha 318.)
Yet this one "inferior" melacha seems to draw an inordinate amount of attention. About a third of tractate Shabbat, and about a third of the laws of Shabbat in the Shulchan Arukh, deal primarily with the laws of hotzaah. And Rav Nachman of Breslav teaches that this prohibition is so important that all of the 39 forbidden labors are included in the prohibition on carrying! (Likutei Halachot Shabbat 7:30.)
Domain of the One, Domain of the Many
The central prohibition of carrying is moving something between "reshut hayachid", a private domain, and "reshut harabim" - a public domain. (See Baal HaMeor, Shabbat chapter 11.) The literal translation of reshut hayachid, "the domain of the one", naturally suggests the domain of the One, those aspects of the world which belong to holiness and God's unity. And the reshut harabim, "domain of the many", naturally suggests the domain of division and separation, those aspects of life where God's unifying influence is hidden. (See Zohar Pinchas III:243b.)
The resemblance is not purely linguistic. The home, the private domain, is a place we can shape and guard, and we can readily make it into an abode for the Divine Presence. The street, the public domain, is a place which we share with other people. Even though most people we share the public domain with are worthy folk, the very fact that any person has the right and ability to enter there makes it a symbol for a place where evil has free reign.
An object which we have placed in a private domain can symbolize an idea or value which we consider positive or holy; an object in the public domain symbolizes something which is evil or profane. So carrying objects between these domains symbolizes the ongoing application of moral criteria to our life experience.
Just as we may find something in our homes and decide it should be thrown out, so we may find something in our hearts which doesn't belong in the character of a righteous person and and work to get rid of it. Conversely, just as we may find an object of value in the street and make it a valuable addition to our home, we may sometimes find an invaluable lesson or value in a seemingly God-forsaken place, and strive to internalize it.
Even in this symbolic understanding, there is a temptation to view carrying as an "inferior melacha". We tend to think that "real" avodat HaShem is actually doing something positive, or fighting some negative temptation. The fact that carrying is considered a melacha can teach us that sometimes our hardest job in working to improve the world is not to change things, but rather to evaluate them, to decide what is right and wrong in the first place.