Latin re‑, red‑, again, back.
In principle, re‑ can be added to any verb to make new verbs or verbal derivatives. The most commonly encountered sense, especially in words of modern creation on English stems, is of something happening or being done once more or afresh: redecorate, re-elect, repeat, re-roof, reprint, retry, rewrite.
Related ideas are of going back to a previous place or state (re-establish, refund, restore, return, revert); of withdrawal or reversal (recant, recede, resign, revoke); or of pushing back or acting against something, opposing (react, rebel, repel, resist)
In a few cases, the older Latin form of red‑ appears, at one time used before vowels: redolent (Latin olere, to smell), strongly reminiscent or suggestive of something; redeem (Latin emere, buy), compensate for the faults or bad aspects of something, or gain or regain possession of something in exchange for payment.
Most words in re‑ are written without hyphens, even when the prefix is followed by a stem beginning in a vowel (reuse, reinsure); however, some do appear hyphenated before e (re-enact, re-enter) though US usage prefers to omit the hyphens.
Hyphenation is used in particular to indicate that repetition is meant, in order to distinguish words with that sense from others with the same spelling with a figurative sense (re-sign, to sign again, say a contract to continue a service, versus resign, to voluntarily leave a job or other position; re-form, to form again, versus reform, to make changes in something in order to improve it). Hyphenated terms in such pairs have a stronger stress on the re‑ prefix.