I have checked your script and working fine, few points for you to check
1.Have you save this script file as "webpage.php" ?
2.Have you repalced "email@example.com" with a valid email address ? - receipient email address
3.Have you ameded the php.ini file for the mail server settings SMTP & smtp_port settings ? following is my setting.
; For Win32 only.
SMTP = 10.10.27.7
smtp_port = 25
4.If you have amended the php.ini, then did you restart your appache to pickup the new settings ?
5. your TO EMAIL ADDRESS in the form is assigned to the FROM EMAIL ADDRESS in the script ? looks not correct
6. you needs to have an echo(); function call for your text -"Thank you for using our mail form";
Hope this helps to trouble shoot