Entering your birth date on your iTunes account -- which is part of your Apple ID -- helps serve an important purpose. If you ever forget the password to your iTunes account, your birth date can help you reset it and regain access to your account. If you entered your birth date incorrectly when you created the account, change it to be accurate. You can't change your birthday through iTunes itself. Instead, you must change your Apple ID account information.
Direct the browser of your choice to the Apple ID (appleid.apple.com) sign-in page. Click "Manage your account" on the right. Sign in using the email address and password associated with your account.
Click the "Password and Security" option located on the left side of the page. This takes you to a page where you can reset your password or change your security questions.
Enter your accurate birth date into the "Select your birth date" fields below the password and security questions sections. Click "Save Changes" when you're done.