a there is a reference to the newly created object that new A() creates. That has nothing to do with the singleton pattern, though; that's always true.
In the singleton pattern, you would find a way of ensuring that new A() is only called once ever in the program. The typical way this is done is to make A's constructor private, and create the instance from within A (which is thus the only class allowed to call the private constructor).
public class A {
public static final A instance = new A();
private A() {}
}
This approach does have a few edge cases, though: you can create extra instances through reflection, and through serialization if A is serializable. To really make a singleton, the best way in Java is to use enums:
public enum A {
INSTANCE;
// fields, methods etc go here
}
The JVM will ensure that only one A.INSTANCE exists in the process.