Karl Marx was an activist and writer, who started off as a radical democrat fighting the Prussian monarchy and the established religion of his time and from the mid 1840s until his death in 1883 became a leading figure in the socialist movement.
The idea of socialism had circulated as an ideal and a speculation long before Marx. Socialism as a political or quasi-political movement originated in the early 19th century. When Marx was a young man, it was growing in vigour and fame, but was still made up of a chaotic scattering of groups with very varied notions of how their more-or-less-shared ideals of socialism could be made reality.
With his friend and comrade Frederick Engels, Marx set out a new conception of socialism in their "Communist Manifesto" of 1848.
They argued that socialism meant the liberation of the working class, and could be made reality only by the struggle of the working class. They saw the struggle for socialism as based on, and a qualitative extension of, the struggle for democracy already underway in capitalist society: "The first step in the revolution by the working class is to raise the proletariat to the position of ruling class, to win the battle of democracy".
In their theory, socialism was not just a good idea, and existing capitalist society was not just a bad state of affairs. Socialist politics were based on the development of contradictions and potentialities built into that existing society.
The circulation of the "Communist Manifesto" was choked off by the defeat of the revolutionary upsurges which started to sweep Europe within weeks of its publication in 1848. Exiled in Britain, and politically isolated for a while, Marx (with the help of Engels) set himself the task of working through thoroughly the task he had indicated in the Communist Manifesto - investigating in sober fact how existing capitalist society worked, and what its contradictions and potentialities were.
That work culminated in the writing of his book Capital in 1867. (It was originally planned as the first volume in a multi-volume work, never completed).
By that time Marx was active in a big socialist-minded movement again, called the International Working Men's Association or First International. He developed many of what he saw as the political conclusions from his theoretical work in debates within that movement. His contributions culminated in his pamphlet The Civil War in France, a defence of the workers' uprising which took power in Paris for nine weeks in 1871 (the Paris Commune).
Repression after the defeat of the Paris Commune destroyed the International, but Marx's ideas continued to circulate. By the time of his death in 1883, sizeable workers' movements in a number of countries saw Marx as their main teacher on how to win socialism.
The term "Marxist" was then still a jeer used by Marx's opponents within the socialist movement, but later most working-class socialist activists came to consider themselves "Marxist", in one sense or another, meaning something like what biologists would mean by describing themselves as followers of Darwin, or physicists as followers of Newton and Einstein.
Even in established mainstream social and historical theory today, Marx is recognised as, at least, a major contributor.
The term "Marxism" has, however, suffered misuse. The Stalinist counter-revolution in the USSR annexed the term "Marxism" for its own use, claimed that Stalin's decrees were the best and only form of "Marxism", and thus applied the description "Marxist" to stances and policies which were the very opposite of the main drift of Marx's working-class socialist ideas.
Click on the link below for a summary of Marx's life and some of his ideas written by Lenin for an encyclopaedia (i.e. for a "general reader") in 1914.