Marx's main claim about religion relates closely to his ideas about society in general. Marx believes that the most important fact about society was the relationship between the classes that make it up. That is the "base." Everything else is simply the "superstructure" that embellishes the base. Everything in the superstructure is made to perpetuate the basic relation between the classes.
Therefore, religion is simply one more thing that is meant to support the dominance of the bourgeoisie. Marx says that religion is a man-made phenomenon. The point of religion is to be "the opium of the people." (This is often seen as "the opiate of the masses.") Marx believes that religion is used by the dominant class to dull the senses of the masses. The masses then stop caring about the fact that they are oppressed in this life because they are more concerned with religious matters.
In this way, Marx's main claim is that religion is simply one more thing that helps the dominant class to maintain its superiority over the lower classes.