The POST data which holds the submitted form data is being echoed in the form, eg:
<input name="firstname" type="text" placeholder="First Name" required="required"
value="<?php echo $_POST['firstname'];?>"
Either clear the POST data once you have done with the form - ie all inputs were ok and you have actioned whatever your result from a form is.
Or, once you have determined the form is ok and have actioned whatever you action from the form, redirect the user to a new page to say "all done, thanks" etc.
header('Location: thanks.php');
exit();
This stops the POST data being present, it's know as "Post/Redirect/Get":
http://en.wikipedia.org/wiki/Post/Redirect/Get
The Post/Redirect/Get (PRG) method and using another page also ensures that if users click browser refresh, or back button having navigated somewhere else, your form is not submitted again.
This means if your form inserts into a database, or emails someone (etc), without the PRG method the values will (likely) be inserted/emailed every time they click refresh or revisit the page using their history/back button.