The phrase ça ne fait rien literally translates as "that doesn't matter." Other French synonyms include, ce n'est pas grave, peu importe, qu'importe, tant pis, and ça m'est égal; but none of these conveys the depth of despair and resignation intended by the original words. Ne fait meaning "doesn't make for", and Rien meaning "nothing". The words are an expression of a resigned, even cynical, acceptance of a sad state of affairs.
The phrase was adopted by the British Tommies in World War I and morphed into the British expression san fairy ann.
The British soldiers who went off to fight in France during the Great War (World War I) popularized the phrase. They soon discovered that despite the popular frenzy, there was nothing great about war. Britain lost almost a million men, and the term Lost Generation refers to the generation of young men who along with their ideals were consumed in the mechanized slaughter. The contrast between idealism and the cold brutal reality of war undoubtedly inspired the phrase san fairy ann among the young soldiers. Many of Britain's best and brightest died, as a civilian population at home eventually learned of brutal trench warfare, gas attacks, senseless mass attacks, and poor generalship.
In 1976, Paul McCartney reprised the phrase, altering the spelling and the meaning, in his song San Ferry Anne. You can also listen to a romantic interpretation of the phrase in French by Alain Chamfort in his song Ca Ne Fait Rien.
Matthew Stewart in his blog Rogue Strands gives a good modern day explanation of the phrase and a poem to boot.