This case was one of the most important cases in Supreme Court history. It was the famous "switch in time that saved nine" (because it helped to diffuse any momentum towards FDR's court packing plan). This was the case in which the Court abandoned its doctrine of "substantive due process" and began to allow the federal government broader powers to regulate the economy based on Congress's constitutional right to regulate interstate commerce.
In 1935, Congress passed the Wagner Act which gave many protections to labor unions and union members. The Jones & Laughlin Steel Corporation fired a number of workers for trying to unionize. The workers sued.
Historically, the Supreme Court had said that the 5th and 14th Amendments protected the right of workers and employers to make any contracts they wanted to between themselves. In other words, they could make contracts for any amount of pay (so minimum wage laws were illegal) or any amount of hours worked (so maximum hours laws were illegal). Similarly, they could make contracts banning union activity. This was seen as part of their liberty and could not be taken away without due process of the law.
In this case, the Court reversed this reasoning. It held, instead, that laws regulating labor relations were legal because of the interstate commerce clause. It stopped using the idea that such laws were illegal under the due process clauses of the 5th and 14th Amendments. This allowed not only the New Deal programs but also has allowed the much more extensive set of government regulations that exist today.