Why did Donald Trump shut down the government?

President Trump refused to sign any appropriations bill—a bill that authorizes the spending of government funds—that did not include funding for his projected border wall with Mexico. The Republican-controlled Senate had originally passed an appropriations bill without border wall funding, and the new Democrat-controlled House of Representatives that took office in January 2019 voted to pass it. But Trump insisted that he would veto any bill that did not provide funding for the entire border wall.
Attempts were made at compromise, and Trump endorsed a stop-gap measure to keep the government open for three weeks to allow some kind of long-term deal to be made. However, no progress could be made during talks between the President and Congressional leaders, as Trump reiterated his demands that any appropriations bill should include border wall funding. And so, at the end of the three week stop-gap period, the government shut down and would remain shut for another thirty-five days.