Well there are many things you could discuss here. Economically Roosevelt instituted many social welfare plans. He essentially was a democratic socialist and greatly regulated the banks of the United States and set up the Glass-Steagel(unsure of spelling) Act which made it to where a bank essentially was unable to use the money that you put into it for risky investment (it was repealed under Clinton and this was a major factor in the recession of 2008, but I digress). There was also the FDIC which insured people's money in banks up to 100,000 dollars I think. It's hard to determine the success of Roosevelt's economic programs though because World War 2 really helped pull the United States out of the Great Depression.
As for the political impact Roosevelt was really the first modern president to gain a lot of control. Now what exactly does this mean? Well before him most of the presidents with the exception of a few such as Lincoln or Andrew Jackson were very weak and Roosevelt was the first President, and this trend continues to today, to really take control of power from Congress even though the framers of the Constitution intended the Legislative branch to be the most powerful. After Roosevelt the executive branch got much larger thanks to the many bureaucratic programs instituted under him and his alphabet soup administration. Roosevelt even had the gall to threaten to raise the judicial branch from 9 to 13 judges so that he could more-or-less force his legislation through and not have to worry about the constitutionality of it.
So in short, economically he made the government have much more control and created welfare programs and politically he greatly enhanced the powers of the presidency and the executive branch as a whole. Hope this helps.