I assume that you are asking about the split in the Republican Party in the 1912 presidential election. In that election, Theodore Roosevelt, who had been a Republican president, ran as an independent while the incumbent president, William Taft, ran as a Republican.
The two most important issues in this split were tariffs and conservation. Many Republicans wanted lower tariffs, but Taft supported the Payne-Aldrich Tariff which did not lower tariffs much. On conservation, the main issue was the firing of Gifford Pinchot. He was the head of the Division of Forestry and was fired essentially for fighting for conservation and against the policies approved by Taft. Both of these actions by Taft were not progressive enough for many Republicans and the party split, allowing the Democrat, Woodrow Wilson, to be elected.