Origins
The English adjective 'high' is one of the fundamental spatial terms of the language and one of the most metaphorically productive words in English. It descends from Old English 'hēah' (with variants 'hēh' and 'hīeh'), from Proto-Germanic *hauhaz, from the PIE root *kewk-, meaning 'to curve, to arch, to vault.' The original image behind 'high' was not linear extension upward but the upward curving of an arch, a hill, or a vault — height as something that rises by arcing.
The Proto-Germanic cognates are uniform in meaning and show the regular sound correspondences: German 'hoch,' Dutch 'hoog,' Swedish 'hög,' Danish 'høj,' Norwegian 'høy,' Icelandic 'hár,' and Gothic 'hauhs.' The German form 'hoch' is particularly instructive because it preserves the guttural fricative /x/ (the 'ch' sound) that English 'high' has lost. In Middle English, 'high' was still pronounced with this guttural — 'heigh' or 'hey-kh' — and the silent 'gh' in the modern spelling is a fossil of that sound, much like the 'gh' in 'night,' 'light,' and 'through.'
The Great English Vowel Shift transformed the pronunciation further. Old English 'hēah' had a long 'ay' vowel (roughly like the 'a' in 'hay'), which Middle English preserved. During the fifteenth and sixteenth centuries, this vowel shifted to the modern diphthong /aɪ/, while the guttural consonant fell silent. The result is a word whose pronunciation (/haɪ/) bears little resemblance to its medieval form but whose spelling preserves the older state.
Old English Period
The noun 'height' shows an interesting irregularity. By regular derivation from 'high,' the noun should be 'highth' (parallel to 'deep/depth,' 'wide/width,' 'long/length'). And indeed, 'highth' was the historical form, used by Milton and others. But the modern form 'height' reflects contamination from a different Old English noun, 'hīehþu' (height), whose vowel displaced the expected one. The result is a spelling that looks as if it should rhyme with 'weight' but is actually pronounced /haɪt/.
In Old English, 'hēah' carried both spatial and social meanings from the earliest attested period. A 'hēah' mountain was tall; a 'hēah' king was exalted; a 'hēah' feast day was important. The association between vertical height and social or moral elevation is one of the deepest and most universal conceptual metaphors in human language. God is 'on high.' The king sits on an elevated throne. 'High' society is the elite. A 'high' crime is a serious one. This vertical metaphor for status pervades English (and most Indo-European languages) so thoroughly that it is difficult to discuss rank, quality, or importance without invoking spatial terms.
The compound 'highway' dates from Old English 'hēahweg,' literally 'high way' — not because the road was elevated but because it was a main road, a road of importance. The 'high' in 'highway' carries the social/hierarchical meaning: the important road, the king's road, as opposed to a local lane or path. This sense of 'high' as 'principal, main' appears in many compounds: 'High Street' (the main commercial street in a British town), 'high seas' (the open ocean, international waters), 'high noon' (exactly midday, the peak of the day), and 'high treason' (treason against the sovereign, the gravest form).
Later History
'Highlands' names terrain that is literally high, and the Scottish Highlands — 'the Highlands' — have been so called since at least the fourteenth century. The distinction between Highlands and Lowlands in Scotland carries not just geographic but cultural, linguistic, and political significance: the Gaelic-speaking, clan-based Highland culture versus the Scots-speaking, more Anglicized Lowland culture.
The slang use of 'high' to mean intoxicated or euphoric dates from the 1930s in American English, initially referring to alcohol and later extending to drugs. The metaphor maps the euphoric feeling onto vertical elevation — to be 'high' is to be lifted above the normal baseline of consciousness. The derivative noun 'high' (a state of euphoria, as in 'a natural high') dates from the 1950s.
In music, a 'high' note is one with a greater frequency of vibration — the spatial metaphor maps pitch onto the vertical axis, with faster vibrations imagined as higher in space. This mapping, while culturally widespread in the Western tradition, is not universal: some cultures describe pitch differences in terms of size (large vs. small) or thickness (thick vs. thin) rather than height.
Latin Roots
The comparative and superlative forms 'higher' and 'highest' are regular, unlike the suppletive forms found with 'good' and 'bad.' The ordinal-like 'uppermost' and 'supreme' compete with 'highest' in some contexts, introducing Latinate vocabulary alongside the Germanic core word. But 'high' itself has never been displaced by a Romance-language equivalent in everyday English — unlike 'poor' or 'strange,' it remains solidly Germanic, a sign of the word's fundamental importance in the language.