What is the origin for left being used to indicate socialist/liberals, and right is used for capitalists/conservatives on the political spectrum?

The French Revolutionary era was where the terms Left-wing politics and Right-wing politics first originated.

The reason for the terms to become used at all was the seating of the ancien régime of France at that time. The aristocrats sat on the right, and the commoners sat on the left. So these terms evolved to mean so that right-wing politics refer to politics for aristocratic and royal interests, while left-wing politics refer to republicanism, socialism, and civil liberties.

It has to do with the French Revolution, and how the various parties arrayed themselves in relation to the King at the National Convention. The less radical revolutionists, the Girondistes, who were more sympathetic than their opponents to the Royalist cause, arrayed themselves to his right, as is traditionally done for guests of honour. The Montagnards, who later evolved into the very radical Jacobin faction, arrayed themselves to the King's left.

It has to do with church relegating the bride to the left side or siniestra (sic. sinister, left) side of the pews during politically arranged marriages. This because monarchs were religiously sanctioned by the church to further the aims of establishing patriarchal order, which sought social control by controlling women, who they married etc. This arrangement also prevailed at royal courts where petitioners also seated themselves according to which side of the appeal they were one. The relegation of the brides family to the left side of the church during weddings, and the view of left handedness as being wrong is still prevalent in today's society.