>>1
there's layman's terms, and then there's layman's "what the guy on the radio says it is". I'll assume you want educated meanings and not political blowhardism which is what the 2 users of newpol give you when they aren't perusing white nationalism sites.
socialism - economic system seeking to ensure well being of all through various means depending on what specific kind of socialism
left wing - those who sit to the left side of the French parliament and wanted to change the system of governance so that there wouldn't be an inherited economic and ruling elite anymore. modern meanings are too numerous to mention.
right wing - those who sit to the right side of the French parliament and wanted to keep the system of gevernance with inherited economic and ruling elite. modern meanings are too numerous to mention.
authoritarianism - system using strong cental command, an authority, a dictator.
totalitarianism - system with extreme authoritarianism, having management of all aspects of society.
conservatism - temperament toward keeping present system or changing only with caution and tentative steps.