Jackie, to clarify, we're not sure if you're talking about your own profile or for a profile you manage for a different person.
If the profile is for a deceased person then you can use public privacy (green), as Natalie explained, in which case biography and sources will all be displayed. If you assign Private for privacy level (which you would have to do for your own profile, since you are living), but make it with public biography, then the biography and sources will all be displayed. If you choose a Private level with private biography, then neither biography nor sources will be displayed.
Essentially, when the word "biography" is used in discussion of whether or not it will be displayed depending on privacy level selection, it really means everything in the big free text box on the edit page, which is essentially the biography AND the sources.