Send input with php

Question

I know, this topic is not new but I have a problem and can't go on. So I would be happy if someone could help me.

I have a form on my website and now, I want to send the input to my email-address. But when I click the submit-button, I got no email and it opens my php code. what is wrong?

That is my html code:

 <form action="sendMail.php" method="post" name="form">
    <table border="0" cellspacing="0" cellpadding="2">
        </tr>
        <tr>
          <td>Vorname:</td>
          <td>
            <input maxlength="50" name="vorname" size="45" type="text" />
          </td>
        </tr>
        <tr>
          <td>Email:</td>
          <td>
            <input name="email" size="45" type="text" />
          </td>
        </tr>
        <tr>
          <td>Mitteilung:</td>
          <td><textarea cols="30" rows="5" name="msg" placeholder="Ihre Mitteilung"></textarea></td>
        </tr>
        <tr></tr>
        <tr>
          <td>
            <input type="submit" name="submit" value="Abschicken" />
          </td>
        </tr>
      </tbody>
    </table>
</form>

And that is my php code:

    <?php
        if(isset($_POST['submit'])){
            $name=$_POST['name'];
            $vorname=$_POST['vorname'];
            $email=$_POST['email'];
            $msg=$_POST['msg'];

            $to='x.y@zzz.com';
            $subject='Form Submission';
            $message="Name :".$name."\n"."Vorname :".$vorname."\n"."Wrote the following :"."\n\n".$msg;
            $headers="From: ".$email;

            if(mail($to, $subject, $message, $headers)){
                echo "<h1>Sent Successfully! Thank you"." ".$name.", We will contact you shortly!</h1>";
            }
            else{
                echo "Something went wrong!";
            }
        }
    ?>

And when I click submit, I get this:

Thats what happen in my browser

Thanks a lot for your help!