Meaning of the Flag

The flag of Nepal is the only national flag which is not rectangular, being based upon two separate pennants which belonged to rival branches of the Rana dynasty, which formerly ruled the country. The two pennants were first joined in the last century, but it was not adopted as the official flag until 1962, when a constitutional form of government was established.

The moon in the upper part represents the royal house. The sun in the lower part symbolizes a branch of the Rana family, members of which acted as prime ministers until 1961.

The charges are now said to represent the hope that Nepal itself will last as long as the sun and the moon. The style of these heavenly bodies was streamlined on December 16, 1962. The coat of arms still portrays these charges with facial features. Crimson is deemed the national color.

Motto on their coat of arms: "The mother and the Mother Earth are more important than the heavenly kingdom."

Why is the Nepali flag the only non-rectangular national flag?

Probably the answer is easier, if the question is asked the other way round: Why are all national flags (except for the Nepali one) rectangular?
The pretty uniform shape of the national flag can be probably explained by the fact that the national flag has its origin in a limited area (Europe and Mediterranean), as ship flags. Certainly there had been different shapes in the early times, but rectangular clothes of an approximate proportion of between 1.5:1 and 2:1 seemed the most practical ones, so the countries "standardized" this shape. Afterwards the ship flags had been adapted for terrestrial use. National flags of countries outside Europe only developed after European national flags had standardized their shape, so they were imitating the rectangular shape as well as some of the symbolic elements (vertical/horizontal stripes, for instance). Older national symbols were transformed to the "European" flag shape, for instance in Ethiopia, where the originally separated red, yellow and green pennants were transformed into a horizontal triband of rectangular shape. Nepal retained the original shape of its flag (basically two pennants one above the other). The first origin of this flag is probably elusive. However, other flags in the Indian area also showed non-rectangular, often pennant-like shape, see in-princ.html#alpha. The Nepali flag is probably the only one surviving, something like a "living fossil". Usually living fossils survive in rather secluded areas, such as Nepal (not having coastal access, and being mountainous) or Switzerland (the same), still sticking to the square shape of its flags.
Marcus E.V. Schmöger, 17 July 2004

The triangular shape reflects the historical shape of flags used by kingdoms on the Indian subcontinent. Even today the flags flown on the masts of temples in India are predominantly triangular.
Armano Grande, 19 March 2008