ועשו לי מקדש ושכנתי בתוכם "They shall make me a sanctuary so that I may dwell among them." The S'forno explains that Hashem will dwell among us to accept our prayers and worship. Ramban says in the Moreh Nevuchim that the Mikdash was built to serve the Jews as an educational tool initially, to stop the Jews from committing idolatry. The later purpose is to show the Jews that serving Hashem is different from serving other gods and to make the Jews closer to Hashem without using intermediaries. Abarbanel says that the building of the Mikdash was a symbolic act. Its purpose was to show the Jews that Hashem does not only live in heaven. He also lives on Earth. The Sefer HaChinuch says the reason we built the Mikdash is that Hashem wanted to establish a place on earth that would help man and increase his merit. According to Chasidism, the Mikdash was built to illuminate the physical world so man's mundane activities could be made holy to Hashem. Rav Moshe Feinstein explains the reason for the Mikdash based on a comment of Rashi on our pasuk. Rashi interprets the pasuk of ועשו לי מקדש ושכנתי בתוכם literally; our purpose is to build the physical structure of the Mikdash, and Hashem will make it holy. Rav Moshe adds that this pasuk actually implies that we, too, have to help make it holy, and we should not merely build the Mikdash and leave it up to Hashem to sanctify it. Based on this we can say that the Torah empowers us to make Hashem dwell among us.
Support for this idea of Rav Moshe begins with can be found in the fact that the Torah first lists the materials to be used in the Mikdash. It should have stated the Mitzvah of building first, and then listed the materials to be used. If the Torah would have first given the Mitzvah to build the Mikdash, it would have implied that Bnei Yisrael were to only give physical donations, but they were not expected to bring any קדושה to it. They would have understood the words ועשו לי מקדש as a command to give financial donations, because the thing immediately following it would have been a list of necessary supplies. The Torah instead opened by asking for materials to be donated. Once the people were prepared to contribute financially, Hashem added ועשו לי מקדש ושכנתי בתוכם. He was telling them that the money and materials which they believed were totally physical must be converted into something spiritual. This was to be accomplished when the donors realized that their money is really owned by Hashem. Thus, something which had been viewed as physical was seen as spiritual. This new attitude of Bnei Yisrael was their way of giving spirituality to the Mikdash, showing that they knew what it meant to donate things for the building of something holy. So too for ourselves, if we seek to come closer to Hashem, this understanding of how to sanctify the mundane is the first step.