The most usual translation, detachment, suggests a serene remove, but this word points to the world-dismay (and so self-dismay) that it is such a strong feature of all the classical south Asian religions. It is both a philosophical and an aesthetic notion: there is vairāgyam poetry (melancholy and satiric) just as there are existential novels.
The metaphor behind it is something like this: a brilliant red cloth is left out in the sun and it bleaches and becomes tattered. The red is sexual passion, ambition for power, greed for wealth. The bleaching is the feeling that these hungers are self-defeating entrapments (along the lines of ‘the hedonic treadmill’ or in a favoured image humans are ‘like moths to a flame’).
The word is built as follows:
rāga colour, specifically red; love, anger, passion
vi indicating change, separation, sometimes complete reversal
(yoga is joining, viyoga is disjoining, separation), so:
virāga loss of colour, dispassion
This word is then converted up onto a more abstract level by adding to the end of the word the marker ya (not unlike poor > poverty) and by at the front amping up the first vowel (not unlike strong > strength = German stark > Stärke). This mechanism is very widely used to build words in Sanskrit: buddha ‘the awakened one’ > baudha ‘buddhist’ or yoga > yauga ‘to do with yoga.’ virāga is already a state (of cloths, of minds): in vairāgyam it becomes an endeavour and a program.
vairāgyam and sun salutes pull in opposite directions, one rejecting the world and the other affirming it (be fit! be well!), but those two impulses have always been chasing each other’s tails: every buddhist monastery was also a business as any tradition that absolutely renounced the world would be immediately defunct, but simply to 'succeed' is not enough.
Patañjali Yogasūtra 1.12 ‘this suppression (of mental formations) is by means of practice and vairāgyam.’`