Ukraine's flag is two bands, blue over yellow, read as the sky above fields of wheat. The design is about as simple as national flags get, and it spent most of the 20th century banned.
Banned, then restored
The colors go back to the 1848 Spring of Nations uprising in Lviv, when Ukrainian nationalists first took up blue and yellow. They became an official flag during the short-lived Ukrainian People's Republic in 1918.
Soviet rule replaced them with Soviet symbols and forbade their use, which is precisely what turned the flag into a symbol of resistance and of a cultural identity that the state was trying to erase. After Ukraine declared independence from the Soviet Union on August 24, 1991, the old colors came back. The flag was raised over the parliament building on September 4, 1991, and parliament confirmed it as the national flag by resolution on January 28, 1992.
Two bands, and what they carry
Blue sits above yellow, each band the same height. Blue is usually read as the sky, and by extension peace, and yellow as ripe wheat, and by extension prosperity.
Other readings exist. Blue has been taken to mean the Dnieper River or the struggle for independence, and yellow to point to Cossack heritage or older wealth. The sky-and-wheat interpretation is the one that stuck.
Display
The flag is flown at government buildings and ceremonies, on national holidays, and at international events. It must not touch the ground and is displayed in a raised, prominent position. Citizens are expected to stand during the anthem and moments of silence. Athletes wrap themselves in it after wins, which is now as familiar an image as any official use.
National Flag Day falls on August 23 and is marked with public ceremonies. The flag was carried through the Orange Revolution and Euromaidan, and it recurs in Ukrainian literature, music, and art.
Similar palettes elsewhere
Kazakhstan and Palau also use blue with yellow, and in both cases the colors point to sky and to wealth or the sun. Older regional symbols using similar combinations may lie behind Ukraine's as well.
References
[1] Government of Ukraine - National Symbols (https://www.kmu.gov.ua/en)
[2] North American Vexillological Association (https://nava.org)
[3] "Ukraine: A History," by Orest Subtelny
[4] Encyclopedia of Ukraine, National Symbols (http://www.encyclopediaofukraine.com)
[5] Scholarly articles on Ukrainian national identity and symbols