When a person builds a building, the first thing that is usually done is to level the site to be able to build on level ground.
The Beis Hamikdash was built on Har Habayis. A retaining wall was built around the mountain and filled in with earth to create a level surface. But the Beis Hamikdash and its courtyards were not built on the flat surface. Instead it was built rising up the slope of the mountain.
As one entered deeper into the Beis Hamikdash complex, they had to climb many stairs. There were 12 stairs from Har Habayis up to the Ezras Nashim. The Ezras Yisroel was another 15 steps higher. Finally, to enter the Sanctuary itself one needed to climb additional 12 stairs to enter the Sanctuary itself.
Each section of the Beis Hamikdash had an increased holiness. This is reflected in the restrictions on who could enter each area and when. Building the Beis Hamikdash on the slope of the mountain shows how these spiritual elevations manifest themselves in the physical elevation as well.
The ultimate purpose of a Beis Hamikdash is for G-dliness to permeate and impact the physicality of the world. In our homes, it means that our relationship with Hashem is not limited to our spiritual experiences. Holiness should reflect itself in the most mundane, physical aspects of our lives as well.