As I understand, new is a keyword and not a function.
For example
A a = new A();
instantiates the object a of type A.
A keyword is not associated with any object per se.
On the contrary, when we have in A a public inner class B we call
B b = a.new B()
Here it looks like new is a property of B and not an independent keyword.
What is the meaning of A.new?
new is a keyword in both cases. It's part of a class instance creation expression.
There are two forms: unqualified and qualified.
The unqualified form starts with the keyword 'new'.
The qualified form starts with a primary class, and then 'new'. This allows creation of inner classes—non-static nested classes that hold an implicit reference to an instance of the outer class. The qualified form provides a way to specify that instance.
From the Java Language Specification, section 15.9:
Unqualified class instance creation expressions begin with the keyword new.
An unqualified class instance creation expression may be used to create an instance of a class, regardless of whether the class is a top level (§7.6), member (§8.5, §9.5), local (§14.3) or anonymous class (§15.9.5).
Qualified class instance creation expressions begin with a Primary.
A qualified class instance creation expression enables the creation of instances of inner member classes and their anonymous subclasses.