For Marx and Engels the notion of class struggle is the key to understanding history. At all stages of history, they argue, there have been power struggles of one sort or another between social classes. In the medieval era, the prevailing class struggle was between feudal landlords and peasants. For many centuries the landlords were on top, achieving an unchallenged position of dominance in society. However, as the economic foundations of society changed over time, a section of the peasantry was able to form itself into a rising middle-class, or bourgeoisie. This sounded the death knell of feudalism and its replacement with a capitalist mode of production.
Capitalism may be radically different from feudalism, but it shares one crucial feature: the persistence of class struggle. Only now the struggle is no longer between landlord and peasant as in the Middle Ages, but between the bourgeoisie and proletariat, or working-classes. At the time when Marx and Engels were writing it was very much the bourgeoisie that was firmly in control; they were the leaders of society as well as enjoying the lion's share of economic and political power.
However, Marx and Engels believed that, in due course, this would all change dramatically. What they called the inherent contradictions of capitalism would eventually lead to a proletarian revolution which would replace capitalism with a communist system. The class struggle would then be over, resulting in the complete abolition of the previous class system.