The word 'light' descends from Old English 'lēoht' (light, daylight, brightness, that which makes vision possible), from Proto-Germanic *leuhtą (light), from PIE *lewk- (light, brightness, to shine). This PIE root is among the most productive and widely attested in the entire Indo-European family, generating words for light, whiteness, vision, and illumination in virtually every branch.
The Germanic cognates are: German 'Licht,' Dutch 'licht,' Old Norse 'ljós' (modern Swedish 'ljus,' Danish 'lys,' Norwegian 'lys'), and Gothic 'liuhaþ.' All derive regularly from Proto-Germanic *leuhtą. The modern English pronunciation /laɪt/ reflects the Great Vowel Shift and the loss of the velar fricative that was once pronounced between the vowel and the final 't' — Middle English 'light' was pronounced roughly /liːxt/, with the 'ch' sound of Scottish 'loch.'
The PIE root *lewk- produced an extraordinary range of words in the classical languages that subsequently entered English. Latin 'lūx' (light, genitive 'lūcis') is the direct Latin cognate, appearing in 'lucid' (clear, full of light), 'elucidate' (to bring to light, to clarify), 'translucent' (allowing light through), and the name 'Lucifer' (light-bearer, from 'lūx' + 'ferre,' to carry — originally the morning star Venus, later applied to Satan in Christian tradition). Latin 'lūcēre' (to shine) produced 'lucent.' Latin 'lūmen' (light, an opening for light) produced 'luminous,' 'illuminate
Latin 'Lūna' (the Moon — literally 'the shining one') is also from *lewk-, making 'lunar,' 'lunatic' (originally 'moon-struck,' driven mad by moonlight), and 'lunate' (crescent-shaped) all relatives of 'light.' The connection between the moon and madness — embedded in 'lunatic' — reflects the ancient belief that the full moon affected human behavior.
Greek 'leukós' (λευκός, white, bright) is the Hellenic cognate, appearing in 'leukemia' (literally 'white blood,' named for the proliferation of white blood cells), 'leucocyte' (white cell), and 'leucine' (a white amino acid). The semantic link between 'light' and 'white' is natural — the lightest color is white, the color of pure brightness.
The figurative extensions of 'light' are fundamental to English and most Indo-European languages: light is knowledge, truth, goodness, and revelation. 'Enlightenment' (the acquisition of understanding), 'to shed light on' (to clarify), 'to see the light' (to understand or to be born), 'a light at the end of the tunnel' (hope) — all exploit the metaphor of light as intellectual and moral clarity, in contrast to 'darkness' as ignorance and evil. This metaphor is not culturally arbitrary; it appears to be nearly universal, rooted in the biological fact that vision — the dominant human sense — depends on light.