Origins
The verb 'reply' conceals within its two syllables a vivid physical metaphor: conversation as folding. Latin 'replicāre' combined 're-' (back) with 'plicāre' (to fold), producing the literal meaning 'to fold back.' In classical Latin, this could mean unrolling a scroll (folding it back to read it again), repeating a passage, or — in legal and rhetorical contexts — answering an argument by 'folding it back' upon itself.
The legal usage was crucial to the word's eventual English meaning. In Roman legal procedure, the plaintiff made his case, the defendant responded, and the plaintiff could then 'replicāre' — fold the argument back by answering the defendant's response. This technical legal sense of 'answering back' was carried into Old French 'replier' and thence into Middle English 'replien,' where it generalized from legal procedure to all forms of response.
The word entered English around 1390, initially in legal and formal contexts. The broadening to everyday conversational response occurred during the fifteenth century. By the sixteenth century, 'reply' was the standard English word for responding to any communication, though it retained (and still retains) a slightly more formal register than 'answer' or 'respond.'
Latin Roots
The connection between 'reply' and 'replica' is one of the more surprising revelations within the 'plicāre' family. Latin 'replicāre' in its sense of 'to repeat' or 'to reproduce' gave Italian 'replica' (a reproduction, a copy, a repeat performance). English borrowed 'replica' from Italian in the eighteenth century as an art term — a copy of a work made by the original artist. The idea is that the artist 'folds back' to the original to reproduce it. A reply in conversation and a replica in art are the same metaphor: folding back to the source.
The computing term 'replication' — as in database replication — draws on the same Latin root and preserves the meaning more faithfully than one might expect. When a database replicates, it 'folds back' data to create an exact copy at another location. The Latin metaphor of folding back to reproduce, first applied to scrolls and legal arguments, now describes the behavior of distributed computing systems.
The phonological reduction from 'replicāre' to 'reply' is typical of the '-plicāre' compounds in English. Just as 'applicāre' became 'apply,' 'complicāre' became... actually, 'complicate' preserved the full form (because it entered English later, as a learned borrowing), while 'comply' reduced it. This double pattern — some words preserving '-plicate' and others reducing to '-ply' — reflects the difference between popular borrowings through Old French (which suffered erosion) and learned borrowings directly from Latin (which preserved more of the original form).