The word comes from Greek εὐφημία (euphemia) "the use of words of good omen", which is a compound of eû (εὖ) "good, well" and phḗmē (φήμη) "prophetic speech; rumour, talk". Etymologically, the eupheme is the opposite of the blaspheme "evil-speaking". The term euphemism itself was used as a euphemism by the ancient Greeks, meaning "to keep a holy silence" (speaking well by not speaking at all).
Reasons for using euphemisms vary by context and intent, and can include avoiding discomfort in day-to-day social interactions, or at an extreme, evading responsibility for war crimes. For instance, one reason for the comparative scarcity of written evidence documenting the exterminations at Auschwitz (at least given the scale) is "directives for the extermination process obscured in bureaucratic euphemisms".
The euphemism affirmative action meaning a preference for minorities or the historically disadvantaged usually in employment or academic admissions (also called reverse discrimination, or in the UK positive discrimination) is an example of a well-intentioned circumlocution to disguise intentional bias that might be legally prohibited, or otherwise unpalatable.
A euphemism such as “enhanced interrogation,” for torture, may be less benign: columnist David Brooks called the euphemisms for torture at Abu Ghraib, Guantánamo and elsewhere an effort to "dull the moral sensibility".
Phonetic euphemism is used to replace profanities, giving them the intensity of a mere interjection.