Please explain how WITH Clause working in a sql query?

An inline view or a query uses subquery in it.
Subquery execution done more efficiently rather by using the query repetadly.
On case by case the performance varies with WITH clause in a sql query.

Below example shows how to reduce repetition of query and simplify complex SQL statements.

SELECT e.ename AS employee_name,
       dc.d_count AS emp_dept_count
FROM   emp e,
       (SELECT deptid, COUNT(*) AS d_count
        FROM   emp
        GROUP BY deptid) dc
WHERE  e.deptid = dc.deptid;

Query will be like as below by using a WITH clause.

WITH d_count AS (
  SELECT deptid, COUNT(*) AS dept_count
  FROM   emp
  GROUP BY deptid)
SELECT e.ename AS employee_name,
       dc.dept_count AS emp_dept_count
FROM   emp e,
       d_count dc
WHERE  e.deptid = dc.deptid;

This way we can make multiple references to the subquery more efficient.

Sometime,WITH clause can be used for a subquery to use as a global temporary table or the query to be use as inline query.

What are Private procedure / functions in a Package ?

A function or procedure in a package which is not declared in package specification, its called as private function / procedure.

Scope of private function /procedure is very limited - on the package itself only.

While in declaring the private procedure/function in package, need to take care that it must be declare first in package declaration part of the package.

create or replace package pack_p1 is
    procedure proc_1;
end pack_p1;

create or replace package body pack_p1 is

    procedure test_proc_1 is
    begin
        dbms_output.put_line('package pack_p1 private procedure');
    end test_proc_1;

    function func_1 is
    begin
        dbms_output.put_line('package pack_p1 private function');
    end func_1;

    procedure proc_1 is
    begin
        dbms_output.put_line('package pack_p1 - proc 1');
        test_proc_1;
    end proc_1;

end pack_p1;