According to Shimon HaTzadik the world stands on Torah, Avoda, and Gemilut Chasadim. Rav Noach Weinberg (may he have a refuah sheleimah) explains that the reality that we are meant to live in depends on the internalization of three concepts. First we must know that there is a Creator with a Plan and Purpose for us, this is achieved via Torah. Then we must pursue closeness with Him, as that is the essence of life - Avodah. Finally, out of our acceptance of Torah and Avoda should flow an understanding that all people were created by one G-d and that we must care for all of G-d's creations - Gemilut Chasadim.
Early in Parshat Trumah we find the words "They shall make me a Mikdash, and I will dwell in THEM". G-d will not dwell in IT, but in US. The Gemorah explains that Hashem is called HaMakom because He is the Place of the world rather than the world being his place. In other words, we mistakenly reference G-d as another thing in this world, like tables, chairs and people. G-d is above and beyond this world.
The Mishkan's major vessels serve as reminders of reality. The Menorah represents Torah. The Mizbe'ach represents Avoda. And the Shulchan represents Gemilut Chasadim (as a table symbolizes the primary vehicle through which we provide for others). The symbols of the Mishkan are the reality through which veshachanti betocham is achieved.
Rabbi Tuvia Charner (z"l) felt that these pillars can be understood broadly. Torah means education, Avodah means work, and Gemilut Chasadim means community. There's a story in Masechet Taanit that tells of a rabbi who was poor. He beseeched G-d and a golden leg fell from heaven. In a dream his wife envisioned a world to come in which all righteous people sat at a table with three golden legs while the table she sat at with her husband had only two legs. She insisted that he return the gold to heaven so that their future reward would remain whole.
Usually tables have four legs, and if they’re missing one they move down to three. The Gemorah in using the number three is conveying the fact that their eternal world would be so severely damaged as to become unstable. The minimal amount of legs needed to hold a table is three. Two legs make for a shaky table. This is why in this tale the table starts with three instead of four legs.
The image of three legs in that story can be carried over to explain the fact that the rabbis chose three things upon which the world rests. They could have broken it down to four or five or ten. But the point is that these three values are so essential to the balance of the world that if one were taken away, the world would falter. Different people favor different pillars. There are Torah people, Tefilah people, and Chesed people. But the ideal and stable individual like the ideal and stable world rests on a balance of three pillars. May we be so blessed.