What does Roosevelt mean when he quotes an English judge as saying "Necessitous [needy] men are not free men?"
What President Roosevelt meant in saying this was that it was important for people to be economically secure in order that they could also have political freedom. When he said this, he was proposing what he called a "second Bill of Rights" in his 1944 State of the Union address.
The US was, of course, in the middle of a war against dictatorships. Roosevelt may also have been anticipating the Cold War against yet another dictatorship. In this part of the speech, he makes the argument that it is necessary to ensure that people have economic security so that they do not become susceptible to dictatorship. The idea was that people who are economically desperate are more likely to support dictatorships because they are willing to trade freedom for (they hope) economic security.