This reading mostly discusses the New Moon sacrifices, as this is the first commandment given to the Israelites. I was intrigued by this passage, though:
1 Thus said the Lord God: The gate of the inner court which faces east shall be closed on the six working days; it shall be opened on the sabbath day and it shall be opened on the day of the new moon. 2 The prince shall enter by way of the vestibule outside the gate, and shall attend at the gatepost while the priests sacrifice his burnt offering and his offering of well-being; he shall then bow low at the threshold of the gate and depart. The gate, however, shall not be closed until evening. 3 The common people shall worship before the Lord on sabbaths and new moons at the entrance of the same gate.....8 When the prince enters, he shall come in by way of the vestibule of the gate, and he shall go out the same way.Interestingly, when the "prince" comes to observe the sacrifice, he bows low and returns the way he came. The commoners, however, go through the inner court and leave by way of the opposite gate. Seems like they get a more intimate experience of the sacrifice than the prince does!
9 But on the fixed occasions, when the common people come before the Lord, whoever enters by the north gate to bow low shall leave by the south gate; and whoever enters by the south gate shall leave by the north gate. They shall not go back through the gate by which they came in, but shall go out by the opposite one. 10And as for the prince, he shall enter with them when they enter and leave when they leave.
It seems that the prince, who may be jaded by the pomp and circumstance of the Temple worship, needs to maintain some distance from the inner court, in order to keep a reverent perspective. The commoners, however, get to experience this only on occasion, and thus are permitted the full experience. The first mitzvah is one of democratization, where the prince bows low at the gate, and continues to bow low as the commoners pass him to go to the opposite gate. The prince is thus reminded that even as he bows to G*d through the sacrifice, he is also bowing to the people.