WordPress uses the PHP mail function to send emails generated by WordPress or any contact plugin. However, the PHP mail function may not be reliable, the most common reason being that your WordPress hosting server is not configured properly. The easiest and most reliable fix is to switch your mail delivery to use the SMTP protocol. That's the standard protocol used by email providers to send outgoing mail.
Switching to SMTP is most easily done with a plugin. There are a number of free SMTP plugins available, and you can find them by searching for "SMTP" at Plugins > Add new. If you're an SMTP novice, we recommend the plugin "WP Mail SMTP by WPForms" as being particularly easy to set up. You can route email through your Gmail account, your hosting provider's mail functionality, or any of a number of popular mass mailer software such as MailGun and MailChimp, and there is good documentation for how to do that.