this is functions.php

function updatePassword($id,$npassword)
{
if(mysql_query("UPDATE `users` SET `password`='".$npassword."'  WHERE `id`=".$id))
    return true;
 else
    return false;
}

this is setting.php

<div class="settingform">
 <form action="setting.php?update=password" method="post">
 <h2>Past Password:</h2> <input type="password" maxlength="100" name="p1"     value="" /><br />
<h2> New Password:</h2> <input type="password" maxlength="100" name="p2" value="" /><br />
 <input type="submit"name="newpasswordSubmit" value="Save" /><br /><br />

                    </form> 
                <?php 

                    if(isset($_GET['update']) && $_GET['update']=="password")
                     {
                   $ppassword =   trim(mysql_real_escape_string(md5($_POST['p1'])));
                        $npassword = trim(mysql_real_escape_string(md5($_POST['p2'])));

                        $errors = array();
                         if(strlen($npassword)>100)
                            $errors = "your EMAIL is too long";
 if($ppassword !== $password) 
                            $errors = "Password did not match";

                        if(empty($errors))
                        {

strong text if(updatePassword($settingUsersData['id'],$npassword)) echo "Updated!";

                            else
                            echo "An Error Has Occurred!";
                        }
                        else 
                            foreach ($errors as $e) 
                                echo $e."<br/>";
                    }
                ?>  
            </div>

I think the problem is in your update function Remove quotes from the field names.

function updatePassword($id,$npassword)
{
 $sql = "UPDATE users SET password='".$npassword."' WHERE id=".$id);
 $result=mysqli_query($connection, $sql)
 $affected_rows=mysqli_affected_rows($result);
 if($affected_rows==1){
   return true;
 }else{
   return true;
  }   

}

I can't see a place in your code that you make a call to this function. Call the function where necessary. (Please do not use mysql. It is deprecated as of PHP 5.5.0, and will be removed in the future.)