It seems that the Torah is simply prohibiting lighting a fire on the Sabbath. The question is, though, why is that necessary? All of the 39 categories of labor forbidden on Shabbat are learned out from the 39 categories of labor required to construct the Sanctuary. The use of fire in cooking the dyes that would be used is one of those 39 categories. There does not seem to be an additional need for this verse, since we already know that it is forbidden to light a fire on the Sabbath.
In truth, there are some reasons why a special verse is required for fire. On holidays, for example, fire is permitted in the service of cooking. So the Torah must specifically prohibit it. Secondly, the creation of fire was the first work done by Adam at the conclusion of the Sabbath. Therefore lighting a fire has a special significance.
But the sages extract a surprising law from this verse. A court is not allowed to impose a corporal punishment on the Sabbath. The explanation is that one of the methods available to the court of capital punishment is Burning. This, therefore, is explicitly prohibited. I might think it should be allowed, because by carrying out such a punishment we are removing an evildoer from the world. Nonetheless, the verse tells us that Burning, and by extension, all other forms of capital or corporal punishment which cause physical injury, are prohibited on the Sabbath.
The commentary Minchat Hinuch, written by Rabbi Joseph Babad who lived about 200 years ago, raises an interesting question. If the Torah's intention was simply to counteract a mistaken idea that capital punishments may be carried out on the Sabbath, why does it create a separate commandment to that effect? We have many examples of limitations on commandments that are learned from Biblical verses that do not rise to the level of a special commandment. Why is this one different?
I would like to add an even more basic question. If the intent was to teach us that capital punishments may not be carried out on the Sabbath, let the Torah say it explicitly. Why phrase it in the context of burning a fire – one of the capital punishments – and then having us extrapolate from there to the other types of capital punishment?
And, of course, why is this located at the beginning of the section describing the construction of the Sanctuary?
My teacher, Rabbi Aaron Soloveichik, of blessed memory, often said that the "true fire of Sinai sheds warmth and sheds light and does not destroy anybody." He was referring to the burning bush which "was not consumed."
Many rabbis see a hint in this prohibition of fire to a warning to avoid fighting and arguing on the Sabbath. "Do not fan the flames of argument on the Sabbath day!" I believe that judgment and argument are intrinsically connected. When people begin to judge each other, the flames of discord are not far away.
A Mishna in the tractate of Negaim (leprosies) : "A person can see all of the cases of leprosy except for his own." Technically, this means that a person cannot decide if their own leprosy is pure or impure. It must be seen by someone else, even if he is a scholar himself. But this Mishna has been expanded by the ethical teachers to mean that a person is quick to spot the deficiencies in the other, but not his own deficiencies. The Vilna Gaon explain this in a clever way. A person's right side is considered the side of his merits, where his left side represents his flaws. Further, it is the nature of the right hand to pull things close and of the left hand to push things away. Thus, when a person stands opposite another person, they are right side is opposite the other's left. Thus, they will pull into themselves the other's flaws. Conversely, they will push away the other one's merits with their left.
But put the same person in front of a mirror, and then his right side is opposite his right side and his left is opposite his left. He will pull close his own merits, and push away his own flaws. When one does this, one judges the other. And, as we see, that judgment will in all likelihood be condemnatory.
Perhaps this is why the Torah uses the imagery of fire to prohibit condemnatory judgment. It is not the ideal fire of Sinai, but it is a necessary phase through which the world must pass. There do have to be judges, and there do have to be judgments. Just not on the Sabbath, because the Sabbath represents the ideal state of the world where there is no judgment. The Sabbath is evocative of the revelation at Mount Sinai. Indeed, our prayer service, which puts the focus on the Torah reading, is constructed as a reenactment of the revelation. Thus, the Sabbath and the Torah are united. As Rabbi Soloveitchik said, "The true fire of Sinai sheds warmth and sheds light and does not destroy anybody."
If there is no judgment on the Sabbath, then what is there? Simply being present. If a person stands in front of another person without pulling their flaws to them and pushing their merits away, they are just being present to that other person. This is very holy. It creates an identification, a bond. The Sanctuary served this purpose. It was a place of the Divine Presence. All human beings, wherever they were in life, could go to the sanctuary and be present to God and each other.
So, perhaps, the lesson to learn for us is to make the Sabbath a day of being present. Being present to ourselves, to our loved ones, and to God. We do not judge, we do not condemn, we do not fight. We just open ourselves up to all of God's creation.