Democracy promotion means that the United States government tries to help other countries become democratic. This means that the people in those countries get to vote for their leaders and have more say in how things are run.
To do this, the United States might send money or people to help with things like setting up voting systems, making sure that people can voice their opinions without being punished, and helping to train public officials.
The United States does this because they believe that having a democracy is a good thing for everyone. They think that people should have a say in how they are governed and that this can lead to a more stable and peaceful world.