I think you have to add the Birthdays calendar to your current main calendar. It reads the birthdays from your Gmail address book.
I've no idea how to get to the Birthdays thingy from the phone, but I can direct you there from a PC;
Open Google Calendar. On the left hand side you will see a heading for Other calendars. Right next to that heading is a little dropdown arrow.. click on it and open "Settings". On the bottom section you will see another heading but the same as before "Other Calendars. Look to the right directly across from there and you'll see "Browse Interesting Calendars", click it. Click on More up top. Now you should see "Contact's birthdays and events". Subscribe to that and it should sync the birthdays you have listed for each of your Gmail contacts.
Back in the Google Now settings on your phone; Tap on the top one "Google Now - all cards". Enable things you wanna have notifications for. Birthdays should be there.
I don't think you need to have the birthday thingy added to your Google Calendar, but I added it on mine.