He explained the problems of his day very well. Marx did several things. He is considered to be one of the founders of modern social sciences, along with Émile Durkheim and Max Weber. Unlike many other intellectuals of his time, he insisted that social theories must be examined through a scientific method to see if they world work. Marx is also notable for writing mostly for the poor and disenfranchised, whereas his contemporaries wrote mostly for fellow intellectuals. A talented economist, Marx helped the world understand capitalism better than anyone since Adam Smith -- for example, he was the first to explain why the previously feudal countries of Europe became industrial economies and capitalist powerhouses. Much of what he wrote about how capitalism works stands up to scrutiny close to 200 years later, leading some to call him the father of economic history. The study of sociology was also highly influenced by Marx's writings.
Although many people today think of him as a dangerously misguided individual, the modern understanding of social science and economics - both liberal and conservative - owes an enormous debt to him and his theories. Similarly, his critiques of capitalism and advocacy of communism seem less applicable in the modern world (not that he is no longer relevant). However at the time he was writing, the conditions for the working class, especially in England (where he wrote Capital), were truly appalling, and much of the ideas and movements that would improve and reform it -- and, ironically, blunt so much of communism's power -- were still considered seditious. A year before he began his studies at the University of Bonn, England transported several men to Australia for forming a union.
Ultimately, what Marx didn't reckon on was the dynamism of democracy in order to effect change. Remember, Marx was writing during a time when there was no minimum wage, no worker protection, no welfare system, no laws against child labor, not anti-trust or anti-monopoly laws, no laws demanding truthful advertising, no laws banning unsafe products, no laws guaranteeing rights to women and minorities (and, in a lot of cases, for Europeans and men, too), and, for most of the world, no voting rights for most people. We have come a long way since Marx's time, and he is arguably vindicated by history.
A good way to understand Marx is that he was a lot like a medical doctor of his time: By the end of Marx's life, medicine had discovered germ theory and understood what caused disease, but although it could now prevent the spread of illness (through quarantine, sterilization of operating rooms, and good public health/sanitation policy), when it came to treating people who were already ill, the doctors couldn't do much better than their grandfathers. Marx figured out what was wrong with the new industrial capitalism, but as far as how to handle it, he couldn't do much better than proposing the kind of utopian socialism that had been presented in the early 19th century, rather than the somewhat odd and piecemeal form of modern social democracy.
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