If you do not see the profile button by some organisation, group or project, you don't have the permissions to view it – nothing to get upset about, it’s just the way it’s supposed to be.
On the profile page you can change your information and settings. For example add your photo, contact details, birthday and decide whether to make them visible to other users or not.
You can also change your password and user interface language.
Organisations also have their own profiles, where their authorised users can modify information.
Read more about it in "Adding an organisation".