When you sign up for an account, a message is sent to your email to verify that you are the account holder.
If you have not received the confirmation email, it may have ended up in your spam or promotional folder. If you can't find it at all, you can resend it from the account settings in "your account" from the web browser or in the app.
If you are under 18 and wish to play Star Stable, you will need your parents'/guardians' permission. When this option is selected, you'll be asked for your guardian's email address and the confirmation email will be sent to them.
The email address must be entered correctly to allow your guardian to access your account.