The New Deal was the culmination of the Progressive Era because it was during the New Deal that the government really took much more of a role in steering the economy and in protecting working people.
For example, in the New Deal, Congress passed the Wagner Act. This act ensured that workers would have the right to join unions and that the unions would have the right to bargain collectively. This was an important step in reducing the power of big companies and enhancing the power of workers. Reducing the power of big companies was a major goal of progressive reforms.
Similarly, during the New Deal, Congress passed the Fair Labor Standards Act. This law set minimum wages for workers and also established maximums on how long they could be required to work. Once again, the government was trying to protect workers from big companies.
In this way, the New Deal can be seen as a culmination of the Progressive Era because the New Deal programs did various things to reduce the power of big business and to help workers.
Under the New Deal, many of the reforms progressives had long articulated, marched for, campaigned for, and even died for became realities. These included a government retirement program that would allow people to grow old with dignity rather than facing impoverishment, as well as the institution of unemployment insurance: these came to fruition with the passage of the Social Security Act in 1934. Progressives had long campaigned for a minimum wage: this passed in 1938, when 25¢ an hour became the lowest wage that a worker could be paid. In 1938, Roosevelt also managed to end child labor, making it illegal (in most cases) to employ children under the age of 14. The New Deal brought in the forty-hour work week, the eight-hour day, and the reality of being paid overtime for work beyond forty hours. It strengthened unions and allowed for collective bargaining. It instituted fair and affordable home mortgages and put in place legislation protecting the money people saved in the bank. In the broadest sense, it legitimized the idea that the federal government has a central role in supporting and bettering the lives of common people and in providing programs to lessen the average person's economic distress.
Most of us could, until recently, hardly imagine what life was like for the average person before the New Deal, though we take most of its programs for granted. The New Deal fulfilled much of the Progressive dream of bringing widespread security and stability to working people as a whole. Policies such as the minimum wage, banning child labor, and ensuring a decent retirement remain very strongly supported to this day.