Marx and Engels wrote: "The history of all hitherto existing society is the history of class struggle" (7). How is "class" defined? Why is it important to understand history through the lens of "class"?

For Friedrich Engels and Karl Marx, modern society was based in conflicting relationships between owners and workers. These conflicts pervaded history. While there had been times in the past where harmony characterized social relationships, in a type of society they called "primitive communism," the basis of that harmony was collective ownership of the means of production.
Once the concept of private property developed, class relations began to develop and became rigid. The people who asserted their power by seizing the means of production—primarily land in agrarian society—effectively pushed aside all the non-owners, and bound them in various types of servitude, as serfs or peons.
Although Europe's feudal ruling classes maintained dominance over the workers, in part by denying them property ownership, the class struggle was not quite as firmly entrenched as it was to become once the Industrial Revolution began. With the increasing concentration of capital in fewer hands, ever more people had to go to work in manufacturing. These people, the proletariat, owned only themselves, and the only thing they could sell was their labor. By doing so, they enriched the owners, or bourgeoisie, and further impoverished themselves. As this process of alienation from the means of production advanced further, and capitalism became a fully developed political and economic system, everything including people was commodified. The full extension of this system resulted in some people not just buying other people's labor—that is, paying them wages—but buying other people or turning people into property—that is, enslaving them. In this respect, although slavery is a cornerstone of capitalism, slaves cannot constitute a class because they cannot sell their own labor, as proletarians do, because the system does not recognize them as persons with any rights.
Marx and Engels were not optimistic that capitalism could be easily dislodged, but they were convinced that ongoing class struggle would lead to violent revolution, after which socialism would replace capitalism in its extreme imperialist form.