Power! To the people!
Amandla, roughly translated, means 'power' in the Nguni languages of South Africa.
On various web-sites, you will find it translated as 'power to the people', 'the power is ours' or even 'power to the majority'. As far as I am aware, this translation is not strictly correct. Amandla by itself should simply be translated as power. The mistake is made so commonly because 'Amandla!' is usually used as part of a traditional call and response, in which one party will call out 'Amandla!', and the other party (or, more usually, parties) will respond with 'Ngawethu' (also sometimes spelt Awethu). As part of this expression, 'Amandla' should be translated as 'power', and 'Ngawethu' as 'to the people' or 'is ours'.
So, Power to the people!, or 'Power is ours'
The saying gained popularity during the time of the apartheid regime in South Africa. Resistance fighters of the time used this call and response to enhance the feelings of solidarity already present within their movement. A good example of its use is given in the text below, which is extracted from a paper on the ANC web-site. The paper describes the events in a South African courtroom on June 12, 1964, when Nelson Mandela, along with eight other ANC members (Sisulu, Mbeki, Motsoaledi, Mlangeni, Goldberg, Mhlaba, Kathrada, and Bernstein), stood trial on charges of sabotage and preparing to begin a guerrilla war:
...on his (Mandela's) first entrance into the courtroom, he faced the packed nonwhite gallery and raised his clenched fist, mouthing the word "Amandla"; many Africans in the audience replied "Ngawethu!."...
...The accused waved to the audience as they descended below the dock. Outside, as on the preceding day, large numbers of police, some with dogs, stood ready to control the crowds and avoid any embarrassing incidents or disorder. Among some 2,000 people present there were only a few hundred Africans who showed their emotions. They responded to news of the verdict with shouts of Amandla Ngawethu! and the clenched fist and upright thumb of the ANC... When Mandela and the others were finally driven away, the crowd again shouted and saluted as the convicted men thrust their fists through the bars and shouted back: "Amandla!"
Although the resistance movement has officially ended, cries of 'Amandla! Ngawethu!' can still sometimes be heard in South Africa. However, the old associations, of violence and rebellion, have generally been replaced with associations of victory and happiness. As such, I have heard people shout it out when reminiscing about the struggle against apartheid, or simply when very drunk...
Related to the modern use of the terms, several books have now been written entitled 'Amandla!', and one of the prize-winners at the Sundance Film Festival 2002 was called 'Amandla: A revolution in four part harmony'. The terms have also been used by various AIDS education foundations, charities, campaigns for equal rights for women, and even a squatters organisation in South Africa. Clearly, the expression is moving out of the underground of armed resistance, and into the sphere of the civil rights movement in general.
With many thanks to Frankie and Gritchka.