PHP Codeigniter - parent::__construct

It will simply execute the constructor of parent class

This is a normal class constructor. Let's look at the following example:

class A {
    protected $some_var;

    function __construct() {
        $this->some_var = 'value added in class A';
    }

    function echo_some_var() {
        echo $this->some_var;
    }
}

class B extends A {
    function __construct() {
        $this->some_var = 'value added in class B';
    }
}

$a = new A;
$a->echo_some_var(); // will print out 'value added in class A'
$b = new B;
$b->echo_some_var(); // will print out 'value added in class B'

As you see, class B inherits all values and functions from A. So the class member $some_var is accessible from A as well as from B. Because we've added a constructor in class B, the constructor of class A will NOT be used when you are creating a new object of class B.

Now look at the following examples:

class C extends A {
    // empty
}
$c = new C;
$c->echo_some_var(); // will print out 'value added in class A'

As you can see, because we have not declared a constructor, the constructor of class A is used implicitly. But we can also do the following, which is equivalent to class C:

class D extends A {
    function __construct() {
        parent::__construct();
    }
}
$d = new D;
$d->echo_some_var(); // will print out 'value added in class A'

So you only have to use the line parent::__construct(); when you want a constructor in the child class to do something, AND execute the parent constructor. Example given:

class E extends A {
    private $some_other_var;

    function __construct() {
        // first do something important
        $this->some_other_var = 'some other value';

        // then execute the parent constructor anyway
        parent::__construct();
    }
}

More information can be found here: http://php.net/manual/en/language.oop5.php

what does parent::__construct or parent::model() do?

these functions do exactly the same, only the construct function used to be named after the class itself prior to PHP5. I say in your example you are extending the Model class (and on some older version of CI since you don't need to use CI_model), if I'm correct in this __construct is the same as model().