I have just got the birth certificate back for my daughter, born on 8/9/18.

I was born in November 1977, making me 40, but on the certificate it states that I am 41.

My wife was born in July 1978 but on the certificate it states that she is 40.

Do you know why this would be the case? 

2018 is your 41st year, 2018 is your wife's 40th year. 

Thanks very much - that explains it.