Why this PHP form is not submitted to email?

Question

This is complete code, above section is PHP code and below is the form, I am trying to send mail on GMAIL ID, I have added proper name to each element, can you please help me in rectifying error or issue with this form.

<?php
$name = $_POST['name'];
$email = $_POST['email'];
$message = $_POST['message'];
$to = 'abcd@gmail.com';
$subject = 'Hello';

$body = "From: $name\n E-Mail: $email\n Message:\n $message"; 

if ($_POST['submit']) {
if (mail ($to, $subject, $body)) { 
    echo '<p>Your message has been sent!</p>';
} else { 
    echo '<p>Something went wrong, go back and try again!</p>'; 
}
} ?>

<form method="post" action="form.php">

<label>Name</label>
<input name="name" placeholder="Type Here">

<label>Email</label>
<input name="email" type="email" placeholder="Type Here">

<label>Message</label>
<textarea name="message" placeholder="Type Here"></textarea>

<input id="submit" name="submit" type="submit" value="Submit">

</form>