To dissect this first let's distinguish what Marxism isn't. While related, Marxism is not socialism. Broadly, socialism is a range of theories that share the common idea of the means of production being democratically controlled by the community. Within the context of Marxism, socialism also has a more specific definition as a theoretical period in history that would act as the transition period between capitalism and communism.
Marxism, again while they are related concepts, is not the same as communism. Communism is similar to socialism in that in it the means of production are commonly owned, but it goes further than that, being a society that is classless, moneyless, and stateless.
Many misconceptions of communism come from the idea that it is authoritarian, which couldn't be further from the truth. In fact, the majority of anarchists also consider themselves to be communists (and often Marxists as well). It is due to the unfortunate results of governments that have labeled themselves as communist that this conception has been created. Clearly, labeling a government as communist is inherently contradictory when communism must be stateless. At most governments can hold communist ideals, aiming towards communism with socialist policies. In reality though, this has often not been the case in governments labeled as such. I and most Marxists are no apologist for the actions of states such as the USSR. The USSR may have originally had socialist aims, but due to the many disadvantageous situations around it, devolved into not the means of production being commonly owned, but in state capitalism. The situation surrounding the USSR has been explained better by many others many other times however, so on that subject I will leave an excerpt that summarizes it well and get back to my original goal in this post of defining Marxism.
What then is materialist philosophy? Marx makes use of dialectical materialism to analyze our world, and from that developed his theory of historical materialism. Dialectics is the process of examining seeming contradictions to find the truth. Materialism, contrasting with the idealism of liberalism, puts matter before thought in its interpretation of the world, concluding that the outside world shapes our thought (this does not however mean that they denied the existence of that outside of the material world, Marxism is not inherently against things such as religion despite popular belief). Together, Marx applied dialectical materialism to the history of human development, creating the theory of historical materialism.
Historical materialism examines the history of human development by way of the social relations of production, or the relationships in which humans must enter in order to survive. Society, according to Marx has gone through different modes of production throughout history, in which the means of production have been divided in different ways into social classes, meaning some classes of people benefit from the fruits of others labor. Society has moved from various systems through the emergence of new classes that seize the means of production. Then this class conflict leads to a new social stage through revolution. A great example of this is the transition from feudalism to capitalism from the rise of the merchant class that usurped the monarch's control over the labor of their serfs.
Marx looks at the course of history so far and from there concludes that it is possible for the proletariat, or working class, to seize the means of production themselves to advance to socialism, and then eventually communism. He is not a determinist however, and does not view historical materialism as a formula in which communism is inevitable, simply that it is one of many potential transitions from our modern capitalism and that in order to ensure the betterment of humanity, we must work forward with those ideals in mind.