What is Chalitzah Signifigance? What does it accomplish, and why is it done?
If a man dies with no children, then his brother should marry the widow. If the brother chooses not to do so, then chalitza is a ceremony whereby the brother and the widow proclaim that he refuses to marry her; the widow removes his shoe and spits, and everyone acknowledges and proclaims accordingly.
So the simplest idea is that in the times of the Torah, the generally preferred approach was for him to marry her. If he chose not to, he would be publicly shamed. (Now in many cases such a marriage really would not be the best idea, but the Torah says do this procedure in all cases.) The Sforno notes the next topic in the Chumash is payment for embarrassing someone: we can shame people in specific cases for specific purposes, as warranted by the Torah; but that doesn't mean we can shame anyone willy-nilly. (And it's only because we're a society that cares about people's honor that shaming means anything.)
Now what is the significance of the shoe and the spitting? The spitting seems to be "ptooey, I'm disgusted that you didn't do the right thing." As for the shoe:
Little Midrash Says quotes Chinuch: The widow says:
I would have been willing to be your good obedient wife and even take your shoes off, but you wouldn't marry me. Ptooey.
- Not politically correct today. The Chizkuni offers this answer, and says "this is the one you give to heretics." Check your local non-Orthodox heretic, I guess...
Chizkuni's other answer, which I would gladly give anyone today; also in the Rashbam, described as "simple and natural":
In Biblical times (see Ruth 4:7), the transaction of an estate was executed by one party handing the other party his shoe. Here the brother forfeits his involvement in his dead brother's memory, thus the widow takes the shoe -- she can now marry whomever she wants. Or perhaps, "usually in a transaction one person gives the other person his shoe. You won't even do that; fine, you just sit there and I'll take it off myself. Ptooey."
Malbim mentions there are all sorts of kabbalistic things going on here, but that it can also be understood intellectually. Rather than reduce this to a soundbite, I'll paraphrase only slightly:
... man differs from animals not in his speech, as some birds speak; not in his intelligence, as many animals are quite intelligent; but in his free will, and ability to apply his intellect to the task of his choosing, even if his nature isn't inclined towards it.
The Gemara (Shabbos 152a) states the a king goes atop a horse, a free man atop a donkey, and a human being atop shoes; a king has dominion over thousands of people, most notably their lives in time of war; a free man has dominion over enterprise; and all human beings have a piece of dead animal that separates themselves from the earth that formed them and informs their natures, as free will allows them to rise above it.
The exception is if the ground is holy, as it was for Moses at the Burning Bush, Joshua on his approach to the Jordan, or the priests in the Temple, then they go barefoot, with no separation between them and the earth [furthermore, in such cases, we surrender our will to that of G-d].
In the Biblical transaction of handing over one's shoe, the message was: I mortgage my human dignity on this transaction; and I shall exercise my will and do everything in my power to see it through.
In the case of Yibum, the Torah itself felt it worthwhile to make an exception to the ban on marrying a brother-in-law. Torah going against its own "nature", so to speak.
And yet this fellow keeps describing himself, and being described by others, as "I don't WANT to do this"; he could exercise free will, but he's just going to do whatever he WANTS.
His sister-in-law therefore removes his shoe -- you never act beyond your basic wants? You shouldn't be wearing this.