reform v.

word-forming element meaning "back, back from, back to the original place;" also "again, anew, once more," also conveying the notion of "undoing" or "backward," etc. (see sense evolution below), c. 1200, from Old French re- and directly from Latin re- an inseparable prefix meaning "again; back; anew, against."

Watkins (2000) describes this as a Latin combining form conceivably from Indo-European *wret-, metathetical variant of *wert- "to turn." De Vaan says the "only acceptable etymology" for it is a 2004 explanation which reconstructs a root in PIE *ure "back."

In earliest Latin the prefix became red- before vowels and h-, a form preserved in redact, redeem, redolent, redundant, redintegrate, and, in disguise, render (v.). In some English words from French and Italian re- appears as ra- and the  following consonant is often doubled (see rally (v.1)).

The many meanings in the notion of "back" give re- its broad sense-range: "a turning back; opposition; restoration to a former state;" "transition to an opposite state." From the extended senses in "again," re- becomes "repetition of an action," and in this sense it is extremely common as a formative element in English, applicable to any verb. OED writes that it is "impossible to attempt a complete record of all the forms resulting from its use," and adds that "The number of these is practically infinite ...."   

Often merely intensive, and in many of the older borrowings from French and Latin the precise sense of re- is forgotten, lost in secondary senses, or weakened beyond recognition, so that it has no apparent semantic content (receive, recommend, recover, reduce, recreate, refer, religion, remain, request, require). There seem to have been more such words in Middle English than after, e.g. recomfort (v.) "to comfort, console; encourage;" recourse (n.) "a process, way, course." Recover in Middle English also could mean "obtain, win" (happiness, a kingdom, etc.) with no notion of getting something back, also "gain the upper hand, overcome; arrive at;" also consider the legal sense of recovery as "obtain (property) by judgment or legal proceedings." 

And, due to sound changes and accent shifts, re- sometimes entirely loses its identity as a prefix (rebel, relic, remnant, restive, rest (n.2) "remainder," rally (v.1) "bring together"). In a few words it is reduced to r-, as in ransom (a doublet of redemption), rampart, etc.

It was used from Middle English in forming words from Germanic as well as Latin elements (rebuild, refill, reset, rewrite), and was used so even in Old French (regret, regard, reward, etc.).

Prefixed to a word beginning with e, re- is separated by a hyphen, as re-establish, re-estate, re-edify, etc. ; or else the second e has a dieresis over it: as, reëstablish, reëmbark, etc. The hyphen is also sometimes used to bring out emphatically the sense of repetition or iteration : as, sung and re-sung. The dieresis is not used over other vowels than e when re is prefixed : thus, reinforce, reunite, reabolish. [Century Dictionary, 1895]

c. 1200, forme, fourme, "semblance, image, likeness," from Old French forme, fourme, "physical form, appearance; pleasing looks; shape, image; way, manner" (12c.), from Latin forma "form, contour, figure, shape; appearance, looks; a fine form, beauty; an outline, a model, pattern, design; sort, kind condition," a word of unknown origin. One theory holds that it is from or cognate with Greek morphe "form, beauty, outward appearance" (see Morpheus) via Etruscan [Klein].

From c. 1300 as "physical shape (of something), contour, outline," of a person, "shape of the body;" also "appearance, likeness;" also "the imprint of an object." From c. 1300 as "correct or appropriate way of doing something; established procedure; traditional usage; formal etiquette." Mid-14c. as "instrument for shaping; a mould;" late 14c. as "way in which something is done," also "pattern of a manufactured object." Used widely from late 14c. in theology and Platonic philosophy with senses "archetype of a thing or class; Platonic essence of a thing; the formative principle." From c. 1300 in law, "a legal agreement; terms of agreement," later "a legal document" (mid-14c.). Meaning "a document with blanks to be filled in" is from 1855. From 1590s as "systematic or orderly arrangement;" from 1610s as "mere ceremony." From 1550s as "a or rank at school" (from sense "a fixed course of study," late 14c.). Form-fitting (adj.) in reference to clothing is from 1893.