The Brazilian flag is green, with a yellow diamond in the center, a celestial globe in the diamond and a white band crossing the globe. Inside the band, the inscription "Ordem e Progresso" (Order and Progress) is seen in green and capitalized. The celestial globe contains 27 stars, one for each state and one for the Federal District.
The current flag is a modification of the imperial flag created in 1822. D. Pedro, the Emperor, was the person directly responsible for it (French painter Jean Baptiste Debre painted it). The green background represented the Bragança dynasty (the Emperor's own family), while the yellow color represented the Habsburg Family of princess Leopoldina (his wife). The diamond shape is a symbol of the Emperor's ties with Napoleon Bonaparte, who used a diamond-shaped flag while fighting.
Originally, the flag had the symbol of the Crown instead of the celestial globe (a crown over a shield, the Cross of the Order of Christ, a blue circle with nineteen stars for each province, a globe with meridians). This was removed after D. Pedro II was deposed and the Republic proclaimed. The military junta which replaced the Emperor flirted with a different design for the flag, but as it was very unpopular (think of a United States flag with green and yellow stripes - that's it), the old flag was restored with the globe instead of the Emperor's symbol. The flag became official on November 19, 1889. There's no official reason for the colors nowadays. Primary schools usually teach the green rectangle is a reference to our nature, the yellow diamond to our wealth and the blue globe to our sky (duh). Although it's not official, this version is very popular.
The globe is supposed to be the sky of Rio de Janeiro on the day the Republic was proclaimed, but in reality it is a representation of the sky as seen from some off-Earth position. Either the astronomer who helped design it (Manuel Pereira Reis) was incompetent or that's a sign of friendship with extraterrestrials, the sky seen from God's eyes or an obscure reference to Hinduism. Pick what seems more likely to you. All of the theories are equally popular. The white band, contrary to popular belief, is not the Equator line. It's merely a place-holder for the motto.
The motto (Order and Progress) is supposedly a quote from Auguste Comte, brought to the flag thanks to the positivists of the time.
The flag is 20 units wide and 14 units high. Each corner of the diamond is 1,7 units away from the closest point in the rectangle. The globe has a diameter of 7 units, with complex rules for placing the stars, which are always five-pointed, with different sizes more or less related to their magnitude. More or less.
There are reference flags so that colors can be copied by flag-makers. Pantone colors are currently unavailable, though.
Until recently, usage of the flag was almost always forbidden except while masted. This is no longer the case. Usage of the flag as clothing, in product labels, or deformed in shape or color was forbidden, but now any use that is not offensive is allowed. It should not be masted at night, except if under proper illumination. It must never be lower than any other flag, it should take the center or left-of-center position. The proper way to get rid of an old flag is by giving it to the Army so that it can be burnt on the Day of the Flag.