"opposite of left," early 12c., riht, from Old English riht, which did not have this sense but meant "good, proper, fitting, straight" (see right (adj.1)). It is a specialized development of the adjective that apparently began in late Old English on the notion of the right hand as normally the stronger of the two, or perhaps the "correct," hand. By c. 1200 this was extended to that side of the body, then to its limbs, clothing, etc., and then transferred to other objects.
The usual Old English word for the opposite of left was swiþra, literally "stronger." "The history of words for 'right' and 'left' shows that they were used primarily with reference to the hands" [Buck]. Similar sense evolution in Dutch recht, German recht "right (not left)," from Old High German reht, which meant only "straight, just." Compare Latin rectus "straight; right," also from the same PIE root.
The usual PIE root (*deks-) is represented by Latin dexter. Other derivations on a similar pattern to English right are French droit, from Latin directus "straight;" Lithuanian labas, literally "good;" and Slavic words (Bohemian pravy, Polish prawy, Russian pravyj) from Old Church Slavonic pravu, literally "straight" (from PIE *pro-, from root *per- (1) "forward," hence "in front of, before, first, chief").
The political sense of "conservative" is recorded by 1794 (adj.), 1825 (n.), a translation of French Droit "the Right, Conservative Party" in the French National Assembly (1789; see left (adj.)).