What happens with cookies in Private Browser mode?

I've never really known exactly what happens with cookies when using Private Browser mode.

In this mode, if you just click to Accept cookies, can they actually do anything? Do they have access to anything or does Private Mode override the Accept button and give them access to nothing anyway?

It would be nice if sometimes I could just avoid the endless turning OFF or discovering that the one little tab allows access to your life's history.

Any help/info much appreciated.