Historical origin of the terms
The terms right and left refer to political affiliations originating early in the French Revolutionary era of 1789–1799 and referred originally to the seating arrangements in the various legislative bodies of France. As seen from the Speaker's seat at the front of the Assembly, the aristocracy sat on the right (traditionally the seat of honor) and the commoners sat on the left, hence the terms right-wing politics and left-wing politics.
Originally, the defining point on the ideological spectrum was the Ancien Régime ("old order"). "The Right" thus implied support for aristocratic or royal interests and the church, while "The Left" implied support for republicanism, secularism and civil liberties. Because the political franchise at the start of the revolution was relatively narrow, the original "Left" represented mainly the interests of the bourgeoisie, the rising capitalist class (with notable exceptions such as the proto-communist Gracchus Babeuf). Support for laissez-faire commerce and free markets were expressed by politicians sitting on the left because these represented policies favorable to capitalists rather than to the aristocracy, but outside parliamentary politics these views are often characterized as being on the Right.
The reason for this apparent contradiction lies in the fact that those "to the left" of the parliamentary left, outside official parliamentary structures (such as the sans-culottes of the French Revolution), typically represent much of the working class, poor peasantry and the unemployed. Their political interests in the French Revolution lay with opposition to the aristocracy and so they found themselves allied with the early capitalists. However, this did not mean that their economic interests lay with the laissez-faire policies of those representing them politically.
As capitalist economies developed, the aristocracy became less relevant and were mostly replaced by capitalist representatives. The size of the working class increased as capitalism expanded and began to find expression partly through trade unionist, socialist, anarchist and communist politics rather than being confined to the capitalist policies expressed by the original "left". This evolution has often pulled parliamentary politicians away from laissez-faire economic policies, although this has happened to different degrees in different countries, especially those with a history of issues with more authoritarian-left countries, such as the Soviet Union or China under Mao Zedong.
Thus the word "Left" in American political parlance may refer to "liberalism" and be identified with the Democratic Party, whereas in a country such as France these positions would be regarded as relatively more right-wing, or centrist overall, and "left" is more likely to refer to "socialist" or "social-democratic" positions rather than "liberal" ones.