The profile system allows you to control key contact details that you may not want to be public, for whatever reason.
These options allow you to control if your email address, phone number and/or office location are displayed on your profile. You can also control what extra metadata is displayed for external systems to consume, such as Facebook, Twitter or Google.
To manage your privacy settings open the 'More options' screen by clicking on the 'More options' link in the top right of your edit profile screen:

Changing your contact details visibility
In the 'More options' screen click on 'Contact details' link in the menu on the left hand side:

From here you can show, using 'On', or hide, using 'Off' your email address, phone number and your office location:

Once you have made your changes, click the 'Close' button and when you next 'Save changes' to your profile your privacy settings will be updated.
Changing your metadata output
Click on the 'Metadata visibility' link in the left menu of the 'More options' screen:

From here enable or disable the output of the different metadata types for your profile:

Changing these settings will not have an effect on how your profile is displayed to a human user, but will affect how it is displayed by Twitter and Facebook and how Google gathers information about your profile.
Once you have made your changes, click the 'Close' button and when you next 'Save changes' to your profile your privacy settings will be updated.
Change Search visibility
You can choose to try and block external search engines from indexing your profile. To do this go to the 'Search visibility' link in the left menu of the 'More options' screen:

Then either enable or disable search crawl indexing:

Note: that not all web crawlers will honour this setting, but the major search engines will however it will take some time for them to pick up this change.
Once you have made your changes, click the 'Close' button and when you next 'Save changes' to your profile your privacy settings will be updated.
Disable your profile
If you wish you can choose to completely disable your profile. This will remove your profile from public viewing.
To do so toggle the 'Profile availability' switch to 'Off':

When you next 'Save changes' to your profile will be hidden from public view and your profile URL will return a page not found error.