If your emails are not being delivered, it is likely that your website is unable to deliver emails. The easiest way to resolve this is to send emails through an SMTP server.
If you have your own SMTP server or wish to send emails through Gmail (or similar), install and configure the Configure SMTP plugin.
If you do not have your own SMTP server or are unsure how to setup the Configure SMTP plugin, we recommend using Mandrill, a free service offered by MailChimp:
Emails should now be properly sent based on the conditions specified.
If you do not wish to use Mandrill or your own SMTP server, SendGrid is another great option.
There are also a large number of other SMTP options available from the WordPress.org plugin repository.