What historical context affected Marx's theorizing?

This is ultimately a question about historical context. Karl Marx was born in 1818, and died in 1883. Answering your question then requires some discussion as to the political, social, and economic trends of the nineteenth century.
Ultimately, the 1800's were shaped by two revolutionary moments. First, there is the Industrial Revolution and Industrial Age. Industrialization began in Great Britain and across the 1800s would spread across Western Europe as well as to the United States, and Marx was living right through this critical moment in history. With this in mind, it should not be surprising that industrialization forms such a critical theme of Marx's work. Marxism itself was a product of industrialization, and it acts both as a tool of analysis which seeks to understand the larger trends and patterns that comprise industrialization as well as a radical and revolutionary attack upon it.
Secondly, we have the French Revolution, unleashed in 1789, whose legacy would result in further revolutions and conflicts between Conservatives and Liberals over the future course of politics. Even after the Great Revolution itself had come to an end, there were numerous smaller outbreaks of revolutionary conflict and fervor (for one example, see the Year of Revolutions, 1848). Even after the French Revolution had ended, its impact was still being felt for a long time afterwards.
Finally, a note about Marx himself: he came out of academia. This is important on two accounts: first of all, there was the radicalism that could be seen within the universities themselves. Students very often seemed to number among the most impassioned supporters of liberal and nationalist ideology, and this was certainly the case in Germany, as can be seen in how:

the Polish Revolt... fueled the imagination of German university students. The movement culminated in a huge meeting in 1832 of 30,000 people... where speakers saluted popular sovereignty. Police foiled an attempt by students to seize Frankfurt... [and] the Confederation's Diet responded by... [bringing] the universities under surveillance. (Merriman, 604)

German universities were a wellspring for political radicalism, and then we have Marx, emerging from that university setting, embodying his own brand of revolutionary radicalism.
Additionally, there is the analytic scope of Marx's work. Calling his own brand of Socialism "Scientific Socialism," we see in his theories of class struggle a reading that embraces and tries to explain all of history, and discern the rules by which societies function and evolve. This likewise shows the impact of his academic training, and his background among the universities.
Citation Note: this answer draws reference to John Merriman, A History of Modern Europe: From the Renaissance to the Present (Third Edition). New York: W. W. Norton, 2010.