There can be many causes. To find out what is the cause some troubleshooting will be required.
Begin with wp-mail smtp disabled.
Please try each fix and answer each question down the list, stop and let
me know if you get it working.
Try the email test on the contact form plugin page. Send the test to the
same email address as your contact form does. What is the result?
success or fail?
After you sent the test email, what did it show on the screen?
there should be a yellow box at the top "Test Message Sent Be sure to
check your email to see if you received it." If it displays anything
about failing, your web server mail function might be broken.
When you installed WordPress did you get a welcome email to your admin
Do you receive other mails like comment notifications from WordPress?
The problem could be after the email is sent. It could be a mail
Some web hosts restrict sending mail unless the "From" address is a
valid address on the same domain.
Try step 3 of the "email not working" in the FAQ
Check that your "email to" address is correct and that the email has not
gone into a spam filter somewhere.
You may need to contact your web host for support with the mail delivery
problem. Check with your hosting provider or mail provider that the
emails aren't being caught in their spam filter.
Try using PHP to send the mail instead of the WordPress mail function.
On the plugin settings page you will find this setting: "Send E-mail function:", try setting this to "PHP", then test the form again. In some cases, this will resolve the problem.
Some people report success with step 4 of the "email not working" in
If none of this worked, answer the questions above and let me know.
I might have more ideas. If you got it working what was it?