Around means that the advice is executed instead of the function. You can still call the original with ad-do-it.
Just to add a small example:
(defun foo (x)
(* 2 x))
(defadvice foo (around bar activate)
(setq ad-return-value
(if (= x 1)
42
(+ 1 ad-do-it))))
(foo 1)
;; 42
(foo 2)
;; 5
(foo 3)
;; 7