Marxism is the name given to the set of political, social, philosophical and economic analyses formulated by Karl Marx and his close friend Friedrich Engles during the 19th Century - ideas which remain influential across the world today.
The basic tenets of Marxist thought hold that history is best understood in terms of class struggle and that the material forces of production in a society forms the dominating influence on the cultural/ideological superstructure of any given society - the mode of production determines the mode of life; for example a nomadic peoples culture will be centred around journeying to find fresh food and pasture, wheras a settled agricultural peoples society will be formed on the basis of their own mode of production. The dominant class in a society, which appropriates the surplus economic product of that society creates and supports the dominant ideology of their society, reinforcing their posisition at its top.
The surplus product of a society is the unpaid labour of the working classes - all those who do not own the means of production and whom must sell their labour in return for wages in order to survive. Capitalists buy this labour under its value which create profit. Eventually this leads to a crisis of 'overproduction' ofteb referred to as a 'recession' or 'slump', at which point the workers are abandoned as they are not employed for either a social need or for personal satisfaction - but for the generation of greater profits.
A Marxist state has never existed and is an oxymoron, as is Communist State, etc etc.
Marxism is a democratic ideology, beleiving that only the movement of the vast majority in individual nations and accross the world can overturn capitalism and create a world organised to provide for need, where a person is not tied like a serf forever to one job no matter how demeaning or pointless and where people give and take "From each according to his ability, to each according to his need".
Marxism shows us that a handful of super rich individuals and companies determine the fate of national democracies and of the world - a world which is being eaten to death by the capitalist system of economic organisation.