It comes from the French Revolution, when members of the National Assembly divided the chamber up into those who supported the king (who would sit on to the president of the assembly's right-hand side) and the revolutionaries and their supporters (who sat to his left). Initially, the terms left and right didn't really denote ideology, but merely seating location. It wasn't until the Third Republic (1870s-80s) that parties started using the terms to communicate political stances/ideology.

It was essentially a product of unintentional self-sorting. A conservative deputy in the National Assembly during the Revolution said, "We began to recognize each other. Those who were loyal to religion and the king took up positions to the right of the chair so as to avoid the shouts, oaths, and indecencies that enjoyed free rein in the opposing camp."

This separation continued even into the next iteration of the French congress (the Legislative Assembly, founded in 1791), despite this new body not sharing any members with the former one. The constutionalists, who saw themselves as the continuation of the Ancien Régime defenders of the pre-Revolution sat on the right, while moderates sat in the center, and those who wanted radical change congregated on the left.

The seating convention went through a few adjustments in the intervening years (various crises changed the composition of the assembly, and it was briefly abolished in the early 19th century). The use of the term to denote ideology spread through Europe in the early 20th century (e.g., it became commonplace in England during the pre-WWII era).