Origins
The word 'laugh' is ancient, visceral, and phonologically scarred — it bears the marks of sound changes that have reshaped English beyond recognition since the Anglo-Saxon period. It descends from Old English 'hlæhhan' (to laugh), from Proto-Germanic *hlahjaną, from PIE *kleh₂k- (to shout, to make a loud sound). The journey from 'hlæhhan' to 'laugh' involved two dramatic changes: the loss of the initial 'hl-' cluster and the transformation of the medial guttural consonant into the modern '-f' sound.
The Old English pronunciation was something like /ˈxlæx.xan/ — it began with a voiceless lateral fricative ('hl-'), a sound produced by blowing air past the side of the tongue, and contained the velar fricative /x/ (like Scottish 'loch') in the middle. The 'hl-' cluster was lost in early Middle English, along with all other Old English initial consonant clusters beginning with 'h-': 'hl-' (as in 'hlāf' → 'loaf'), 'hr-' (as in 'hring' → 'ring'), 'hn-' (as in 'hnutu' → 'nut'), and 'hw-' (which survived longer as 'wh-'). The medial /x/ underwent different changes in different dialects: in most of England it became /f/ (giving 'laugh'), while in Scotland it was retained as /x/ (giving dialectal 'lauch').
The spelling 'laugh' with its silent 'gh' is thus a fossil — it records a consonant that was once pronounced as a guttural fricative but has since become /f/ in standard English. The same history explains 'cough,' 'rough,' 'tough,' and 'enough,' all of which have '-gh' representing a lost /x/ that became /f/. Meanwhile, 'through,' 'though,' and 'dough' lost the consonant entirely. The inconsistency of English '-gh' spellings is one of the great torments of English-as-a-second-language learners.
Proto-Indo-European Roots
The PIE root *kleh₂k- (to shout, to make noise) connects laughter to sound-making in general, not specifically to amusement. This suggests that for the earliest Indo-European speakers, a laugh was categorized as a type of shout — a loud vocalization — rather than as an expression of a particular emotion. The emotional specialization ('laugh' = 'make noise because something is funny') developed within the individual branches.
The Germanic cognates are transparent: German 'lachen,' Dutch 'lachen,' Old Norse 'hlæja' (→ modern Icelandic 'hlæja,' which preserves the initial 'hl-'), Gothic 'hlahjan.' The pan-Germanic distribution confirms the Proto-Germanic reconstruction *hlahjaną with high confidence.
The noun 'laughter' comes from Old English 'hleahtor,' with the same initial 'hl-' and the same guttural consonant. 'Laughable' (worthy of being laughed at) dates from the sixteenth century. 'Laughingstock' (a person subjected to ridicule) dates from the sixteenth century as well, from the image of a person locked in the stocks — a wooden frame for public punishment — while bystanders laugh. The phrase 'laugh all the way to the bank' (to profit while others scoff) is mid-twentieth-century American English.