Teddy Roosevelt offered a one-two punch of "good government"at home, and a robust foreign policy. Not all Presidents are good at either domestic or foreign policy; few are good at both.
Domestically, Roosevelt was a great conservationist and arguably the father of the environmental movement ("Teddy" bears are named after him). He was characterized as a "trust buster", preventing large corporations from establishing a stranglehold on the American economy. Though from a rich family, he authored the "Square Deal" for the common man.
In foreign policy, Roosevelt was noted for his quote "speak softly, and carry a big stick". The "naturalist" started the building of the Panama Canal, after acquiring the Canal Zone from Panama, whose independence he won from Colombia, in effect, "connecting" the east and west coasts of the United States. He put America on the map by negotiating a peace between Russia and Japan, and preventing a war between Germany and France over Morocco. (If he had been President in 1914, he would have greatly shortened World War I by immediately intervening on the Allied side, sparing the world part of a great tragedy). He also sent the Great White Fleet around the world, starting in Asia, then Europe, thereby putting Japan on its best behavior for a generation.