Hi, Betsy
Do you mean your birthday is actually a part of your email address? Or are you referring to personal information that you included when you opened the email account with your provider?
If it's the former, the only way to change it is to change the address and that might entail opening a new account.
If you mean the latter, you'll have to go in to your account settings (whoever your provider is) and change it there.
One more option I just thought of is if you actually have your birthday showing in the "from" address when you send an email, even though it's not part of the email address itself. If this is the case, you should be able to change that in your provider's 'account settings' page, as well.