In Marx's view of the world, history has been a series of struggles of class against class. One class dominates, another is dominated. In our current state of development, Marx argued that there are two major classes, the bourgeoisie and the proletariat. The bourgeoisie is the dominant class in our current capitalistic system.
What distinguishes the bourgeoisie from the proletariat is that the bourgeoisie owns the means of production. Meanwhile, the proletariat uses the means of production to create goods. The bourgeoisie do not contribute labor, but take most of the wealth that is created by the labor of the proletariat.
So, Marx says that the bourgeoisie is the dominant class in our current system. They are the class that owns the means of production and that hires people from the proletariat to work for them.