Why were the ideas of Marx and Engels in The Communist Manifesto radical?
A radical idea is one that advocates some sort of truly fundamental change in the way a society is set up. Marx and Engels' ideas fit this definition perfectly.
Marx and Engels weren't arguing that workers should be treated better by their bosses. They weren't arguing for a 40 hour week or a minimum wage or health and safety standards, though those would have been nice for workers at the time. They weren't even arguing for unionization. Instead, they were calling for a revolution in which the workers rose up and took away the property of the bourgeoisie. They were saying that private property should be abolished and the means of production should belong to the workers collectively. In other words, they were advocating a change that would have been truly fundamental to their society. That makes their ideas radical.