Theodore Roosevelt was the first of the progressive presidents (the others were Taft and Wilson). Roosevelt's progressivism was the basis of his domestic policy.
Roosevelt wanted to rein in the power of big businesses and to be somewhat more fair (as he saw it) to workers. These desires were behind the most important aspects of his domestic policies. Important policies of his included "trustbusting" and a more even-handed policy towards labor disputes. It was Roosevelt who first used the Sherman Antitrust Act to try to fight monopolies. It was Roosevelt who first had the government arbitrate a strike (coal strike of 1902) instead of sending in the troops to help the employers.
In these ways, Roosevelt's domestic policies were based on his progressive beliefs.