The display of birthdays and anniversaries can be activated or deactivated in the Calendar List (manage calendars).
In the settings for birthdays and anniversaries, these can be filtered to show only starred / favorite contacts. The favorites are drawn from your phone's contact list and can be edited there.
You also have the option to display the zodiac signs for the respective birthday in the detailed view.
There is also a link to the associated notification settings.
See also: