Well, that's what your oncologist is for--to explain things in terms you can understand. Never let him, or her, get out of the room with a term undefined. :-)
As I understand it, "cancer free" is the equivalent of NED (no evidence of disease). That means that they couldn't find any evidence that you still have cancer.
"Remission" means that the cancer is knocked down and beaten up. It isn't in position to attack you right now. It might attack in the future, but for now all is happiness.
Functionally, these often mean the same thing. It depends on the cancer. If a cancer is curable (not all are but I believe most breast cancer is), then "remission" wouldn't be used unless you are "cancer free." My WM isn't curable so "remission" (not a term used by my oncologist) is what my cancer was until yesterday. Now it's back and I have to beat it into its cave again. :-)