error occuring while inserting data into database using php in codeigniter

When using a class, if you are defining variables, you need to use a access specifier with it. Like in this case :

 class Members_model extends CI_Model 
    {
       $user = 'Vinayak';
       $pass = 'ggf';

should be :

 class Members_model extends CI_Model 
    {
      public/private/protected $user = 'Vinayak';
      public/private/protected  $pass = 'ggf';

and is you use this variable in same calss you can use them like $this->user, $this->pass

Apart from the access level as @Sankalp said, which is what's causing the error you shown, you have a problem in your insert method (you've been blocked by the missing acces specifier, but when you go on, you'll get that error too)

So,

class Members_model extends CI_Model 
{
  private $user = 'Vinayak';
  private $pass = 'ggf';
  // though, why creating class defaults for user and password?? what's the point?

Then, your function:

  function put_members()
  {     
    $this->username = $_POST['user'];
    $this->password = $_POST['pass'];
    $this->db->insert('users', $this);
  }
}

Is wrong: you're passing to the insert() method the whole object ( $this ) when you have to pass the fields names instead:

A better way to do that would be:

function put_members()
{

   $this->user = $this->input->post('user');
   $this->pass = $this->input->post('pass');
   $this->db->insert('users', array(
                                      'user' => $this->user, 
                                      'pass' => $this->pass
                                    )
                    );
}

Where 'user' and 'pass' are the column names of your 'users' table (change accordingly to your setup).

Important note: Let's not talk now about you storing the password in cleartext, which is really bad practice, but keep in mind that as soon as you have your model functioning you should focus on that issue too: use the best solution your php installation provides (crypt() with BLOWFISH would be pretty nice) or at the very very least sha1()