Please follow instructions below:
1) Please check plugin's settings '/wp-admin/admin.php?page=contact_form.php'
2) It is possible that email messages are detected like a spam on the
server. Instead of administrator 'email' choose another 'email'('Use
this email:' block) - for example, gmail account or similar. If the
message will be approved (it will be sent), then you've an email
filtering configured on your server.
3) Perhaps you didn't configure email sending by an extra plugin
called WP-mail-SMTP. The plugin has fields for send verification email, so please set up the plugin, so that email can be send.