Static methods in Java are methods that belong to the class itself rather than any object instance. You call them using the class name, like MathUtils.square(4). When called, the method runs its code using the input parameters, then returns a result or void. In the example, the static method square takes an integer x, calculates x times x, and returns the result. Variables inside static methods are local to the method. Static methods cannot use 'this' or access instance variables because they have no object context. This makes static methods great for utility functions that don't need object data. The execution table shows the method call, calculation, return, and completion steps clearly. The variable tracker shows how 'x' and 'result' change during execution.