What does Atticus mean when he says that professional people are poor because the farmers are poor? Harper Lee's To Kill a Mockingbird.

The above answer does a good job. In chapter two of the book, Jem asks Atticus a question: "Are we poor?" 

Atticus responds in the affirmative. Then Jem asks if they are poor like the Cunninghams. Atticus responds by saying that the Cunninghams are poorer, because they are country folks. The Depression has hit them the hardest. Professionals, like Atticus, are also poor, because they are not paid for their services in money, because the country people do not have any money. 

This is why Mr. Cunningham paid Atticus with goods. In this same chapter the children watch Mr. Cunningham pay Atticus in goods. Here is the text:

We watched. One morning Jem and I found a load of stovewood in the back yard. Later, a sack of hickory nuts appeared on the back steps. With Christmas came a crate of smilax and holly. That spring when we found a crokersack full of turnip greens, Atticus said Mr. Cunningham had more than paid him.

Atticus, then, also points out that many other professionals have done the same thing. For example, Dr. Reynolds charges country folks a bushel of potatoes to deliver babies. 

In short, professionals are poor, because the whole economic system is suffering. Little money is exchanged. So, these professionals work for little.