Codeigniter Sql Error

$this->db->get() must contain an table name. in your case you want to remove it sindse you have an custom query so your function wil look like this:

function get_result_professions($key_word)  
{  
    $sql = "SELECT users.name FROM users 
            inner join users_has_professions  on users_has_professions.users_id  = users.id 
            inner join professions on users_has_professions.professions_id  = professions.id  
            where professions.key_word = '$key_word'  ";


    return   $this->db->query($sql);
} 

The $this->db->get() method in CodeIgniter's Active record requires a table name parameter (see the Active Record Documentation for more info) when used to query a table, unless you have previously build up the query using one of the other provided methods.

Usually when building up joins like you are doing you would use the select/ join methods provided by Active Record, like so

$this->db->select('users.name')->from('users')
    ->join('users_has_professions', 'users_has_professions.users_id  = users.id')
    ->join('professions', 'users_has_professions.professions_id  = professions.id')
    ->where('professions.key_word', $key_word); 

(untested as I don't have your database to run it against)

You can then use the $this->db->get() method to retrieve the results like so

$results = $this->db->get();
foreach($query->result() as $row) {
    //code here
}