This is a great question. A lot of people discuss Marxism and its various elements. However, rarely do people talk about the goals of Marxism. In summary, the goal of Marxism is threefold.
First, Marxism desires to abolish classes in whatever form they exist. Marx and his followers have seen the injustices perpetuated through a class system. The rich get richer and the poor get poorer. So, by not allowing inheritances to continue, Marxism sought to deal a heavy blow to the class system.
Second, the direct corollary to the first point is the importance of economic parity among people. In other words, one group of people will not be ahead of another. Equality will be the central feature of society, which leads to our next point.
Third, the working class will no longer be exploited. Part of the way this would be accomplished is by having the means of production owned by the state. The same would be true of land. All land would be public land for cultivation. The central government would also control communication, transportation, and credit.
Finally, I should add that another main tenet of Marxism is to give free education to all.
The aim of Marxism is to force upon the laborers in society an awareness of their exploitation by the bourgeoisie, the managerial class. Once the people become aware of this exploitation, they will be in the position to overthrow the oppressors and bring about a new type of society. As an Enlightenment thinker, Marx believed that reason could be used to make man's life in society better. He ultimately wanted, as do Marxists generally, a better and more equitable society. So, this is the second 'aim' of Marxism, the first being to get the laborers to recognize their enslavement to the capitalist class.
This is a great question.