The administration claims it has something to do with the US and Iraq agreeing on other (unspecified) security measures to ensure that those "with criminal or terroristic intent" in Iraq don't reach the US.
Here is CNN's story: Why Iraq was removed from the revised travel ban:
Tillerson described his efforts in public remarks Monday after the new order had been signed.
"Iraq is an important ally in the fight to defeat ISIS, with their brave soldiers fighting in close coordination with America's men and women in uniform," he said. "This intense review over the past month identified multiple security measures that the State Department and the government of Iraq will be implementing to achieve our shared objective of preventing those with criminal or terroristic intent from reaching the United States."
The Associated Press, on the other hand, reported that it was due to pressure by the Pentagon and State Department:
Four officials told The Associated Press that the decision followed pressure from the Pentagon and State Department, which had urged the White House to reconsider Iraq's inclusion on the list given its key role in fighting the Islamic State group.
The reason behind the pressure is unclear, but the same article mentions that it may have to do with the fact that Iraq was considering "reciprocal measures" after the first ban was announced:
After Trump signed the original order, Iraqi Prime Minister Haider al-Abadi said he would consider reciprocal measures. Many Iraqi lawmakers urged the government to ban Americans from Iraq in response, despite the potential effects that might have on the anti-IS fight.