The New Deal expanded the authority and responsibility of the federal government in a number of ways. In general, it gave the federal government the power to intervene in the economy in practically any way it wanted and it gave the government the responsibility for ensuring the basic welfare of the people.
Through the New Deal, the federal government got the authority to intervene in the economy in many ways. For example, the government could tell farmers how much of their crops to produce or not to produce. It could force banks to pay into a deposit insurance fund. There are many other examples of what it could to to intervene in the economy.
At the same time, the government took responsibility for the welfare of the people. It did this most clearly through the creation of Social Security. This and other programs established the idea (which has only grown since then) that the government is responsible for ensuring that people have a certain basic standard of living.