Theodore Roosevelt was the 26th President of the United States of America, and served from 1901 to 1909.
He believed that the president's role was really to lead the country, doing good by its people, having more authority. The other presidents believed that the power that wasn't granted was forbidden, and Roosevelt believed the opposite was true: the power that wasn't forbidden was granted.
This is what he means when he says that the president must act even if he doesn't have a certain authorization. He's not saying he's above the law, but that the president must do more than he's assigned to do, if it's for the good of the people.