Gemara: That which it says in the mishna that there are thirty-nine categories of work that are forbidden on Shabbat – what does the number correspond to? Rabbi Chanina bar Chama said: It corresponds to the work done in constructing the Mishkan.

Ein Ayah: Anything that can be used to stimulate the mind and bring new ideas into the world must have come into existence because Hashem wanted it that way. The ideas are always reminiscent of things throughout the physical and spiritual world, and therefore the comparisons can inspire people’s spiritual side.
When many specific elements fit into one inclusive set, it must be that there is some piece of logic that unites them all, and this unifying force must be connected to something else in existence. The connection should not just be technical but should have a logical element to it so that finding the similarity will give a positive result. That is why the gemara raised the question, with the expectation of a good answer: What do the thirty-nine melachot correspond to?

Preparing the World for Completeness
(condensed from Ein Ayah, Shabbat 4:4)

Ein Ayah: The rest and the sanctity that are part of the experience of Shabbat engender blessing and sanctity in the world because they emanate from the ever-existing Master of All, Hashem, who is complete to the fullest degree. Certainly, then, the goal of that which He created must be complete.
The leading element of all existence is the point of sanctity, which is the center of the life of everything that exists. The point of the divine plan is that the greatest projects should be prepared and completed and there should be no need for further actions to deal with that which is missing or lacking.
When Bnei Yisrael needed to create a center of sanctity, there were many types of work that needed to be done because this is what was dictated by the fact that the world was in a lowly state. If not for the triumph of overcoming the obstacles that can destroy an elevated life of sanctity and closeness to Hashem, the collective cannot reach its goal.
Shabbat raises a person to the heights that resemble that which will be in future, ideal times, when all days are like Shabbat. In those times, one will not have to teach his counterparts about Hashem because all, whether young or old, will know about Him. Therefore, the elements of ceasing from work on Shabbat are parallel to the work that is needed to be done to prepare the Mishkan.