The flag of Sudan is a horizontal tricolor of red, white, and black with a green triangle at the hoist. It was adopted on May 20, 1970.
Two flags, two answers to the same question
The first flag of independent Sudan, flown from 1956, was a blue, yellow, and green tricolor. It said nothing in particular about the region, and that turned out to matter: it left the new country without a visible position on where it belonged.
The 1969 coup led by Gaafar Nimeiry supplied an answer. The flag adopted the following May took the Pan-Arab colors, which had been popularized by the Arab Revolt against Ottoman rule and were by then in use across the Arab world. Swapping one flag for the other was a foreign policy statement as much as a design change.
The colors and the name
Red is the blood shed in the struggles for independence. White is peace. Green, in the triangle at the hoist, is Islam, prosperity, and the agriculture the economy depends on.
The black band is the most literal element on the flag. "Sudan" comes from the Arabic bilad al-sudan, land of the blacks, so the black stripe is the country naming itself.
Flying it
The flag is displayed on government buildings, in public spaces, and at national events. Protocol requires that it be hoisted during daylight hours and lit if it is flown at night, that it never touch the ground, and that it fly above any other flag displayed with it. Government departments and military units use variants carrying their own insignia.
Similar flags
Plenty of Arab states use red, white, black, and green, and Sudan's flag is most often compared with Egypt's and Yemen's, which arrange the same colors in horizontal bands. The green triangle is what sets Sudan's apart. It also carries no star or crescent, which several other flags in the region do.
In Sudanese life
The flag is the object people gather around at national celebrations and commemorations, and it turns up in music, writing, and public art. In a country with as many ethnic groups and cultures as Sudan has, that shared reference point does more work than it would elsewhere.
References
[1] Government of Sudan - Ministry of Information (sudan.gov.sd)
[2] Flag Institute's Guide to Flags of the World (flaginstitute.org)
[3] Smith, Whitney. "Flags Through the Ages and Across the World."