The people responsible for the attacks were traced to a terrorist group called Al Qaeda, who believed the United States was a threat to Islamic culture. The American airspace was immediately closed to all commercial flights and Operation Enduring Freedom began, initiating the War on Terror. Airport security in the days and weeks afer was insanely tight and the Transportation Security Administration (TSA) was founded a couple months after.
The psychological effects were devastating as well. People were chilled to the bone, horrified, and even angry that people could do something like this.