Origins
The preposition 'on' is one of the most common words in English, expressing contact with a surface ('on the table'), continuation ('carry on'), and temporal location ('on Monday'). Its etymology connects it to a PIE root for 'upon' that produced important derivatives in Greek and other branches of the family.
It descends from Old English 'on' (on, upon, in, into, at, to — a broader semantic range than the modern word), from Proto-Germanic *ana (on, upon), from PIE *h₂eno- (on, upon). This root is distinct from PIE *h₁en (in), the source of English 'in,' though the two prepositions have overlapping semantic territory and occasionally conflated in Old English, where 'on' could mean 'in' in certain contexts.
The cognates across the Indo-European family preserve the 'upon' sense clearly. German 'an' (on, at, to) is the direct cognate, used for contact and proximity: 'an der Wand' (on the wall), 'an der Universität' (at the university). Dutch 'aan' (on, to, at) shows the same function. Gothic 'ana' (on, upon) preserves the fuller Proto-Germanic form. Greek 'aná' (ἀνά, up, upon, back, throughout) is the classical cognate and has been enormously productive as a prefix in English scientific and philosophical vocabulary.
Proto-Indo-European Roots
Through Greek 'aná,' the PIE root *h₂eno- generated a large family of English words. 'Anatomy' is from Greek 'anatomḗ' (ana + temnein, cutting up — dissection). 'Analysis' is from 'análysis' (ana + lysis, a loosening up — breaking something apart into components). 'Anabaptist' is from 'anabaptizein' (ana + baptizein, to baptize again — upon a second time). 'Anachronism' is from 'anachronismós' (ana + chronos, against time — something placed in the wrong time period). 'Anarchy' is from 'anarchía' (an- + archḗ, without a ruler on top — though the 'an-' here is actually the negative prefix, not 'aná').
Within English, 'upon' is a compound of 'up' + 'on,' and its redundancy testifies to the weakening of 'on' in certain contexts — speakers felt the need to reinforce it with 'up.' The phrasal verb system of English makes heavy use of 'on' as a particle indicating continuation or activation: 'carry on,' 'go on,' 'hold on,' 'turn on,' 'put on.' In these uses, 'on' has shifted from spatial contact to metaphorical persistence — to be 'on' is to be active, engaged, in progress.
The stability of this word across the Germanic languages is notable. Old English 'on,' Old Norse 'á' (on), Old High German 'ana' (on), and Gothic 'ana' (on) all preserve the same preposition with minimal phonological change, reflecting its extremely high frequency and simple phonological structure.