A profile is a member's public section of your site, for example example.com/jane. Everything a member adds goes on a profile: blog posts, audio, photos and so on. When someone signs up, they get a user account and a profile with the same name. Either name can be changed later.
Which sections a profile has (Blog, Audio, Forum, ...) depends on its quota: a module's section only shows on profiles in quotas where it's allowed (see Quotas). Key Concepts explains profiles, user accounts and quotas together.
The profile's owner changes it on its Profile settings page (in the user menu, or the profile's settings button):
The default privacy for new profiles is set per quota with Default Profile Privacy in ACP > Modules > Profiles > Profiles > Quota Config.
Admins see an Admin Options section on every profile's settings page: