In common with many frequent words, the words left and right have more than one meaning. As well as referring to the side that is east when you are facing north, right can also mean, among other things, “correct”, “morally correct”, “immediately” or “completely”.
Left is not quite so rich – apart from its directional meaning, it is the past tense and past participle of the verb to leave. But both words are used to signify a particular political position.
If we want to know why conservatives are to the ‘right’ while liberals are to the ‘left’, we have to go back over 200 years, to Europe around the time of the Revolution in 1789. The National Assembly members in France sat in a semicircular chamber, facing the president of the Assembly. The position of honour was on the president’s right and was occupied by the nobles, while to his left were the commoners.
Politically, the nobles were staunch supporters of the church, the king and the existing constitution, while the commoners were more likely to be anti-church, anti-royalist and in favour of overthrowing the constitution. In between them sat the moderates.
So the right came to represent those political parties that favour continuity and stability (as they see it) while the left represents radical parties of change.