Did you set a Go to page to be redirected to after the email is sent?
If so, are you redirected to that page?
What is the action of the form on your page? It should be left blank so the form will post to itself.
What is the method of the form? It should be set to POST
If all of those check out, then double check the SMTP server that you entered, make sure it is the correct one for your host.
try checking the "Include From Address as an additional parameter" option. your host may require this.
Make sure that the From address and the too address are not the same, some hosts will not relay email messages where the from and too addresses are the same.
If you getting redirected and still not seeing the message, you will need to check with the host, see if they can look into the SMTP server error logs to why the email message is not being relayed.