Hi there:
If the form is working properly, it will both send an email to the email address noted in the contact form and add it to your Feedbacks section on your Dashboard. If no email address is specified in the contact form, the email will be sent to the email address associated with the user account that created the post/page that the form was inserted into.
Can you let me know what site you're having this problem? Once I have that information, I'll be better able to help.
If you want it to remain private, you can also contact us via this contact form:
http://jetpack.me/contact-support/
Thanks!