I often encounter sites with hosting setups which prohibit the use of default PHP mail functions (which WordPress relies on to send emails) - often cheap or shared hosting environments disable this in order to reduce the scope and quantities of email spam activities originating from their shared hosting packages
This problem usually comes to light when a few comments or form submissions have been submitted to the site, but nobody's receiving any email notifications. There's a nifty plugin called WP-Mail-SMTP, which leaps to the rescue in this scenario by providing a highly configurable approach to using SMTP mail in place of PHP's
Install, configure addresses & credentials, and it seamlessly hooks into
wp_mail() to manage the delivery process.