Something isn't right in your example.
class Foo {
    public static void main(String[] args) {
        String x = "foo";
        getString(x);
        System.out.println(x);
    }
    public static void getString(String output){
        output = "Hello World"
    }
}
In the above program, the string "foo" will be output, not "Hello World".
Some types are mutable, in which case you can modify an object passed into a function. For immutable types (such as String), you would have to build some sort of wrapper class that you can pass around instead:
class Holder<T> {
    public Holder(T value) {
        this.value = value;
    }
    public T value;
}
Then you can instead pass around the holder:
public static void main(String[] args) {
    String x = "foo";
    Holder<String> h = new Holder(x);
    getString(h);
    System.out.println(h.value);
}
public static void getString(Holder<String> output){
    output.value = "Hello World"
}