This formula will give you a result like

"Next birthday is 123 days away". On birthday it says "Happy Birthday!"

=IF(DATEDIF(C1,TODAY(),"yd")=0,"Happy Birthday!","Next birthday is "&DATE(YEAR(C1)+DATEDIF(C1,TODAY(),"y")+1,MONTH(C1),DAY(C1))-TODAY()&" days away")

where C1 contains date of birth