Nepal is the only country whose national flag is not a rectangle, and the shape is the oldest thing about it.
From temple pennant to national flag
The design grew out of Hindu banners flown in the kingdoms of the Kathmandu Valley: simple red pennants carrying celestial symbols, used by the ruling dynasties. The Rastriya Panchayat resolved on the current form on December 16, 1962, as Nepal moved to a constitutional monarchy, and the aim was to bring the various states under a single representation. Later work fixed the proportions and colors so the flag could be reproduced consistently.
Two pennants, a sun and a moon
Two triangular pennants overlap, one above the other. The upper carries a white moon with eight rays and a crescent beneath it; the lower carries a white sun with twelve rays. The crimson background is Nepal's national color and stands for the bravery of its people, and the blue border for peace and harmony. The outline is usually read as an echo of Hindu pagodas and of the Himalayas.
Flying it
The flag flies at government buildings, military camps, and public offices, and goes up across public and private spaces during national holidays and at festivals such as Dashain and Tihar. The upper pennant must be at the top. Displayed vertically, the base should face east, in line with traditional ideas about auspicious orientation.
References
[1] Government of Nepal, Ministry of Foreign Affairs. "National Symbols of Nepal." (official site)
[2] International Federation of Vexillological Associations (FIAV). "Symbolism in Flags." (organization site)
[3] Flags of the World. "Nepal." (website)