iCloud: Show the Birthdays calendar in iCloud
Calendar includes a special Birthdays calendar that can display all birthdays that you have in iCloud Contacts.
In iCloud Calendar, click the Action pop-up menu in the sidebar, then choose Preferences.
In the General pane, select “Show Birthdays calendar,” then click Save.
To show or hide the Birthdays calendar, select or deselect it in the sidebar. You can also see the Birthdays calendar on your iOS devices and Mac computers by selecting it in the Calendar app.
To modify a birth date, make the changes in iCloud Contacts; changes are reflected in iCloud Calendar within a day. For more information, see Edit a contact in iCloud.