This Java program demonstrates recursion by defining a static method called test that takes an integer parameter i. The test method recursively calls itself, decrementing i each time, until i is less than 1. It then prints the current value of i before returning. When the main method calls test with an initial value of 4, it causes test to recursively call itself multiple times, decrementing i each iteration and printing the values, resulting in the output of the numbers 4 through 1 being printed multiple times.