Origins
The word 'when' is the temporal interrogative adverb in English, asking about time, occasion, and circumstance. It descends from Old English 'hwenne' or 'hwanne' (when, at what time, whenever), from Proto-Germanic *hwannē, from a PIE formation on the interrogative stem *kʷó- with a temporal or circumstantial element.
The PIE interrogative stem *kʷó- generated temporal interrogatives across the Indo-European family through various suffixation strategies. Latin 'quando' (when) preserves the stem with a different suffix. Gothic 'ƕan' (when) is the most faithful Germanic cognate. German 'wann' (when) and Dutch 'wanneer' (when) show the same root. The consistency of this formation across branches indicates that the pattern of deriving temporal questions from the basic interrogative stem is ancient.
Within the English system, 'when' occupies the temporal slot in the interrogative paradigm: 'what' asks about things, 'who' about persons, 'where' about place, 'when' about time, 'why' about cause, 'how' about manner. Each has a demonstrative counterpart: what/that, who/that, where/there, when/then, why/therefore, how/thus. The when/then pair is particularly transparent: 'when' asks 'at what time?' and 'then' answers 'at that time.'
Old English Period
A revealing etymological fact connects 'when' to 'than.' In Old English, the demonstrative counterpart to 'hwenne' (when) was 'þonne,' which served double duty as both 'then' (at that time) and 'than' (compared to that). The comparative use developed naturally: 'X is bigger then Y' originally meant 'X is bigger at-that-point-where Y is measured.' During Middle English, the spelling and pronunciation diverged, with 'then' retaining the temporal sense and 'than' taking the comparative sense. But they are historically the same word — the demonstrative answer to the interrogative 'when.'
Latin 'quando' (when) produced derivatives that entered English through Romance borrowing: 'quandary' (a state of perplexity — possibly from a Latin scholastic phrase meaning 'when shall I?' indicating indecision about when to act, though this etymology is debated). More transparently, Latin 'quam' (how much, to what degree, than), closely related to 'quando,' contributed to English 'quantity' (how much), 'quality' (of what kind — from 'quālis'), and 'quantum' (how much — used in physics for the smallest discrete amount).
The temporal use of 'when' also extends to conditional and causal senses: 'when you put it that way' means 'if/since you put it that way,' not 'at the time you put it that way.' This semantic extension from temporal to conditional is cross-linguistically common — French 'quand' (when) can similarly shade into conditionality, and German 'wenn' means both 'when' and 'if.' Time and condition are conceptually adjacent: specifying the time of an event and specifying the conditions for it both constrain its occurrence.