try{
  $db = new PDO('mysql:host=localhost;dbname=questionnaire', 'root', '', array(PDO::MYSQL_ATTR_INIT_COMMAND => 'SET NAMES utf8'));
}catch(Exception $e){
  echo 'Erreur : '.$e->getMessage().'<br />';
  echo 'N° : '.$e->getCode();
}

$question1 = $_POST['question1'];


$query = $db->prepare("INSERT INTO form (question1 )
VALUES ('".$question1."')");

   $question1 = isset($_POST['question1']) ? $_POST['question1'] : array();
foreach($question1 as $reponse1) {
    // here you can use $value
    $query->bindValue('question1', $reponse1, PDO::PARAM_STR);
}
  $query->execute();

  <div class="col-md-6">
      <label for="question1">
        <input id="question1" type="checkbox" class="form-control" name="question1[]" value="A">
        A
      </label>
      <label for="question1">
        <input id="question1" type="checkbox" class="form-control" name="question1[]" value="B">
        B
      </label>
      <label for="question1">
        <input id="question1" type="checkbox" class="form-control" name="question1[]" value="C">
        C
      </label>
    </div>