The code for current-kill

The current-kill function is used by yank and by yank-pop. Here is the code for current-kill:

(defun current-kill (n &optional do-not-move)
  "Rotate the yanking point by N places, and then return that kill.
If N is zero and `interprogram-paste-function' is set to a
function that returns a string or a list of strings, and if that
function doesn't return nil, then that string (or list) is added
to the front of the kill ring and the string (or first string in
the list) is returned as the latest kill.
If N is not zero, and if `yank-pop-change-selection' is
non-nil, use `interprogram-cut-function' to transfer the
kill at the new yank point into the window system selection.
If optional arg DO-NOT-MOVE is non-nil, then don't actually
move the yanking point; just return the Nth kill forward."

  (let ((interprogram-paste (and (= n 0)
                                 (funcall interprogram-paste-function))))
    (if interprogram-paste
          ;; Disable the interprogram cut function when we add the new
          ;; text to the kill ring, so Emacs doesn't try to own the
          ;; selection, with identical text.
          (let ((interprogram-cut-function nil))
            (if (listp interprogram-paste)
              (mapc 'kill-new (nreverse interprogram-paste))
              (kill-new interprogram-paste)))
          (car kill-ring))
      (or kill-ring (error "Kill ring is empty"))
      (let ((ARGth-kill-element
             (nthcdr (mod (- n (length kill-ring-yank-pointer))
                          (length kill-ring))
        (unless do-not-move
          (setq kill-ring-yank-pointer ARGth-kill-element)
          (when (and yank-pop-change-selection
                     (> n 0)
            (funcall interprogram-cut-function (car ARGth-kill-element))))
        (car ARGth-kill-element)))))

Remember also that the kill-new function sets kill-ring-yank-pointer to the latest element of the kill ring, which means that all the functions that call it set the value indirectly: kill-append, copy-region-as-kill, kill-ring-save, kill-line, and kill-region.

Here is the line in kill-new, which is explained in The kill-new function.

(setq kill-ring-yank-pointer kill-ring)