Marxism is a socio-economic method of analysis created by Karl Marx and Friedrich Engels. It was created in the 19th century. Their philosophy focuses on economic and social inequality in relation to capitalism and how capitalism is responsible for such inequitable distribution of resources via exploitation of surplus labor. Their theories present an alternative model of socio-economic distribution by ensuring that the means of production are owned by the workers themselves and thus preventing theft of labor. This is of course a very simplified explanation of the system
Marxism describes classes that arise under capitalism. These classes are the Bourgeoisie/Capitalist class, the proletariat or the working class and the Lumpenproletariat or the class that is generally in poverty, Frantz Fanon called them the wretched of the earth.
The Bourgeoisie/Capitalist class are the owners of the means of production under capitalism and as such are oppressors of the other classes. They use their resources and power to ensure the survival of capitalism through many means, including the creation or support of other axes of oppression.
The working class, think factory workers, food service, construction, anyone who works for a boss. These people work for said boss for a set wage, this wage is always significantly less than the value of labor they provide for that boss. That difference is known as wage theft. This wage theft takes place via economic coercion. Because we live in a capitalist society, there are few to no options to find work that pays a wage that is close to the value that you produce. This is why the capitalist class uses their power to try to eliminate non-capitalist systems.
While Marx believed that this class was unlikely to evolve class consciousness later followers of marxism felt that this class could not only develop that consciousness but that this was essential to overturning a capitalist system. The young lords and the black panther party applied this belief in practice. The poorest and most oppressed under capitalism had the most to gain by promoting a socialist system.