There were a number of issues in the 1912 campaign that would have been of interest to progressives.
First, there was the issue of government regulation of the economy, particularly with regard to antitrust issues. Roosevelt wanted to increase government's regulatory power, creating strong and permanent agencies to police the large companies. By contrast, Wilson wanted to have the government break up the monopolies and then step back and let competition take over.
Second, there was the issue of direct democracy. Roosevelt, running as the candidate of the Progressive Party (aka "Bull Moose Party") wanted more direct democracy and wanted it on the national level. He wanted things like referendums and direct primaries. These were things that progressives were interested in because they felt such things would give the people more control of the government, taking the power away from special interests.