This Java program handles mouse events by implementing the MouseListener interface. It displays text on an applet that changes when different mouse events occur - on mouse press the text and position changes to "to" at coordinates 150,150, and on mouse release the text changes to "gmrit" at coordinates 200,200 by calling the repaint method. The program imports necessary libraries, defines the applet class with init and paint methods, and implements mouse event handler methods to update the displayed text and coordinates in response to clicks and presses.