This will be a problem with your PHP file. Normally it will be set up to send the message, sender’s email etc with the email, so make sure that’s set up properly.
This is a PHP question, so if you need more help, click the little orange flag in the bottom left of this post and request that the thread be moved to the PHP forum. In that case, post your PHP file too, so that people can tell you what’s wrong.
Or you can PM your PHP code to me, if you prefer, and I’ll have a look, although I’m no expert in this. Looks like it’s pretty simple to fix, though. 
PS: I think your form fields are too black. They are hard to distinguish and may confuse many users. I also wouldn’t put a naked email address on your page either, unless you LOVE spam. 