Apparently, the idea started out as a joke. "I said, 'Maybe we need a new force, we'll call it the Space Force,' and I was not really serious. Then I said, 'What a great idea,' maybe we'll have to do that," the president said. He continued to discuss why the Space Force would be a good idea. It's unclear whether the president was joking.
White House Deputy Press Secretary Hogan Gidley responded to our request for clarification with the following statement: "The President announced America's new National Strategy for Space includes the recognition of space as a 'warfighting domain.' The National Space Council's mission reflects President Trump's priority to protect the security, commercial, and scientific benefits of space for the American people. We look forward to continuing the conversation on how to best ensure lasting U.S. leadership and success in space."
Joke or not, President Trump isn't close to the first person to discuss militarizing space. The Air Force already has a Space Command division that oversees our country's military operations in space. While militarizing space is a bad idea for many reasons, it's already happening. Director of National Intelligence Daniel Coates said in 2017 that "Both [China and Russia] will continue to pursue a full range of antisatellite (ASAT) weapons as a means to reduce US military effectiveness."
President Trump didn't give us any details about what exactly the Space Force would do. He said, "We may even have a Space Force, develop another one, Space Force. We have the Air Force, we'll have the Space Force." This isn't the first time such a military organization has been suggested; language that would divide the Air Force into two different branches was proposed back in 2017, but ultimately didn't make it into the defense authorization bill.
Update: This article was updated with a statement from the White House.