PHP - Header Location, Issue. Small Piece Of Code, Can Anyone Take A Look

Hi there, i have an code
 

<?php
$a = [
  0 => 10,
];
$i = 0;

$a[$i++] = $i;

and question "Explain what the problem is and what you could do to fix it"

I read this and I totally not understand what it for and how it use and what problem hidden here.
 

Please help!
 

<?php session_start();?>

<?php
include("passwords.php");

//this statement will be entered if coming from the login.php page.
if ($_POST["ac"]=="log"){

	//check if submitted username and password exist in $PASSWORD array
	if ($PASSWORD[$_POST["username"]]==$_POST["password"]){
	
		//set various session variables
		$_SESSION["username"]=$_POST["username"];
		$_SESSION["firstname"]=$FIRSTNAME[$_POST["username"]];
		$_SESSION["lastname"]=$LASTNAME[$_POST["username"]];
		$_SESSION["email"]=$EMAIL[$_POST["username"]];
	}
	else{

	//if username and password do not exist, set session variable for "incorrect username/password" message and redirect to login.php
		$_SESSION['incorrect'] = "incorrect";
		header('Location: login.php');
	};
};

// check if user is logged in already when they are coming from a random place. If not, redirect to login.php
check_logged();
?>

          <div>
            <h3>Login</h3>
            <form method="post" action="process.php" id="sublogin">

                  /* error message should be displayed here when username is empty or == username */
                  <p>
                  <?php
                  echo $form->error("user");
                  ?>

                  <input class="loginside" type="text" name="user" value="username" /> ?> <br />
                  <input class="loginside" type="password" name="pass" value="password" /> <br />
                  <input type="hidden" name="sublogin" value="1">
                  <input type="checkbox" name="remember">Remember me <br />
                  <input class="sublogin" type="submit" value="login" style="border: 0; margin: 5px 0 0 1px;" />
              </p>
            </form>
            Not registered yet? Sign up here!
          </div>

class Process
{
   /* Class constructor */
   function Process(){
      global $session;
      /* User submitted login form */
      if(isset($_POST['sublogin'])){
      	      	
      	      	
				$this->procLogin();
        
      }

      /**
       * Should not get here, which means user is viewing this page
       * by mistake and therefore is redirected.
       */
       else{
          header("Location: index.php");
       }
   }
   
   function procLogin(){
   
      global $session, $form;
      /* Login attempt */
      $_POST = $session->cleanInput($_POST);
      $retval = $session->login($_POST['user'], $_POST['pass'], isset($_POST['remember']));
      
		if($retval){
			header("Location: correct.php");
		}
		else{
		$_SESSION['value_array'] = $_POST;
                $_SESSION['error_array'] = $form->getErrorArray();
                header("Location: index.php");
		}

                /* if instead the $_SESSION and header I enter echo $form->error("user")
                   then the error message is displayed in process.php, and not in index.php
                */
   }

   
 }
 
$process = new Process;

?>

<?php

include "database.php";
include "form.php";

class Session

{
		var $time;
		
		function Session(){
			
			$this->time = time();
			$this->startSession();
			
		}
		
		function startSession(){
			
			$session_name = 'sec_session_id';   // Set a custom session name
	    $secure = true;
	    
	    // This stops JavaScript being able to access the session id.
	    $httponly = true;
	    
	    // Forces sessions to only use cookies.
	    if (ini_set('session.use_only_cookies', 1) === FALSE) {
	        header("Location: ../error.php?err=Could not initiate a safe session (ini_set)");
	        exit();
	    }
	    
	    // Gets current cookies params.
	    $cookieParams = session_get_cookie_params();
	    session_set_cookie_params($cookieParams["lifetime"],
	    $cookieParams["path"], 
	    $cookieParams["domain"], 
	    $secure,
	    $httponly);
	        
	    // Sets the session name to the one set above.
	    session_name($session_name);
	    session_start();           		 	// Start the PHP session 
	    session_regenerate_id(true);    // regenerated the session, delete the old one. 
		}		
		

		function login($subuser, $subpass, $subremember)
		{
			global $database, $form;
				
			/* username check */
			$field = "user";
			if(!$subuser || $subuser == "username")
			{
            $form->setError($field, "* Username incorrect");
			}

			/* password check */
			
			/* if e-mail welcome, check if user activated account */
      	
     	/* Return if form errors exist */
      if($form->num_errors > 0){
         return false;
      }	
      
      return true;
      
		}

		
		function cleanInput($post = array()) {
       foreach($post as $k => $v){
            $post[$k] = trim(htmlspecialchars($v));
         }
         
         return $post;
   	}
			
};

$session = new Session;
$form = new Form;

?>

<?php 
/**
 * Form.php
 *
 * The Form class is meant to simplify the task of keeping
 * track of errors in user submitted forms and the form
 * field values that were entered correctly.
 *
 * Written by: Jpmaster77 a.k.a. The Grandmaster of C++ (GMC)
 * Last Updated: August 19, 2004
 */
 
class Form
{
   var $values = array();  //Holds submitted form field values
   var $errors = array();  //Holds submitted form error messages
   var $num_errors;   //The number of errors in submitted form

   /* Class constructor */
   function Form(){
      /**
       * Get form value and error arrays, used when there
       * is an error with a user-submitted form.
       */
      if(isset($_SESSION['value_array']) && isset($_SESSION['error_array'])){
         $this->values = $_SESSION['value_array'];
         $this->errors = $_SESSION['error_array'];
         $this->num_errors = count($this->errors);

         unset($_SESSION['value_array']);
         unset($_SESSION['error_array']);
      }
      else{
         $this->num_errors = 0;
      }
   }

   /**
    * setValue - Records the value typed into the given
    * form field by the user.
    */
   function setValue($field, $value){
      $this->values[$field] = $value;
   }

   /**
    * setError - Records new form error given the form
    * field name and the error message attached to it.
    */
   function setError($field, $errmsg){
      $this->errors[$field] = $errmsg;
      $this->num_errors = count($this->errors);
   }

   /**
    * value - Returns the value attached to the given
    * field, if none exists, the empty string is returned.
    */
   function value($field){
      if(array_key_exists($field,$this->values)){
         return htmlspecialchars(stripslashes($this->values[$field]));
      }else{
         return "";
      }
   }

   /**
    * error - Returns the error message attached to the
    * given field, if none exists, the empty string is returned.
    */
   function error($field){
      if(array_key_exists($field,$this->errors)){
         return "<font size=\"2\" color=\"#ff0000\">".$this->errors[$field]."</font>";
      }else{
         return "";
      }
   }

   /* getErrorArray - Returns the array of error messages */
   function getErrorArray(){
      return $this->errors;
   }
};
 
?>