The flag of Palau is a light blue field with a golden-yellow disk on it, set a little toward the hoist rather than in the middle. It was adopted on January 1, 1981.
A flag for a new republic
The date marked Palau's move to self-government, out of the Trust Territory of the Pacific Islands that the United States had administered. Decolonization was working its way across the Pacific at the time; Palau's own arrangement was settled later, with the Compact of Free Association signed with the United States in 1994.
The design came from a public competition, which is worth noting: the flag Palauans ended up with was one they chose rather than one handed down by an administering power. It arrived at a point when Palauans were asserting cultural and political autonomy in a number of ways at once.
The moon on a blue field
Light blue is the ocean and the sky, the two things that define daily life on a small island nation, and the color is also read as peace and tranquility.
The yellow disk is the moon. Its cycles have long governed when Palauans plant, harvest, and fish, and Palauan folklore ties the moon to fertility and the harvest. The off-center placement is one of the things that separates Palau's flag from the other circle-on-a-field designs it gets compared with: Japan's, and among its neighbors the Federated States of Micronesia. Blue and yellow show up across Pacific flags generally.
Where it flies
The flag is used at government buildings and on national holidays, most visibly on Independence Day and Constitution Day. Protocol covers position and handling. There are no separate variants for different branches of government; every arm of the state uses the same flag.
References
[1] Palauan Government Official Website: palaugov.pw
[2] North American Vexillological Association: nava.org