word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
1570s, "having a meaning," from Latin significantem (nominative significans, present participle of significare "make known, indicate" (see signify). Earlier in the same sense was significative (c. 1400). Often "having a special or secret meaning," hence "important" (1761). Related: Significantly. Significant figure is from 1680s. Significant other (n.) attested by 1961, in psychology, "the most influential other person in the patient's world."