In some cases, the color of the passport tells you something about the country's values: Saudi Arabia, Pakistan, Bangladesh, and Indonesia all use green, the color of Islam, as do a number of other Muslim-majority countries.
In other cases, passport colors demonstrate alliances — or hoped-for alliances. Members of the Economic Community of West African States have green passports. Member states of the European Union have burgundy passports — so do states that have aspired to join the EU, including Turkey, Macedonia, and Albania, which changed their passports for what the Economist described as a "branding exercise."
Another cluster of burgundy passports, in South America, represents the Andean Community — Bolivia, Colombia, Ecuador, and Peru — as well as former member Chile. Next to the Andean Community is Mercosur, a customs union of Brazil, Argentina, Paraguay, Uruguay, and Venezuela; its passports are blue. (Venezuela, a former member of the Andean Community, still has a burgundy passport, but you get the idea.)
South African passports switched from blue to green in 1994 with the formation of the post-Apartheid government. (At least in some circles, the passport is known as the "green mamba," after a poisonous snake, because of the difficulty South Africans face obtaining visas — although it's worth noting that a South African passport offers greater global entrée than passports of most African nations.)
It's not uncommon for passport colors to change: The US has used red and green in the past and didn't settle on blue until 1994.