An assertion is a statement in the JavaTM programming language that enables you to
test your assumptions about your program. For example, if you write a method that calculates the speed of a particle, you might assert that the calculated speed is less than the speed of light.
Each assertion contains a boolean expression that you believe will be true when the assertion executes. If it is not true, the system will throw an error. By verifying that the boolean expression is indeed true, the assertion confirms your assumptions about the behavior of your program, increasing your confidence that the program is free of errors.
(reference- java.sun website)
http://java.sun.com/j2se/1.4.2/docs/guide/lang/assert.html