// load column titles with the column visibility state into the check list box
var
  I: Integer;
  Index: Integer;
begin
  CheckListBox.Clear;
  CheckListBox.Items.BeginUpdate;
  try
    for I := 0 to DBGrid.Columns.Count - 1 do
    begin
      Index := CheckListBox.Items.Add(DBGrid.Columns[I].Title.Caption);
      CheckListBox.Checked[Index] := DBGrid.Columns[I].Visible;
    end;
  finally
    CheckListBox.Items.EndUpdate;
  end;
end;

// set the columns visibility according to the check list box states; note that
// the whole code shown here relies on the order of the items in the check list
// box which cannot be changed (so you cannot use it for column reordering)
var
  I: Integer;
begin
  DBGrid.Columns.BeginUpdate;
  try
    for I := 0 to CheckListBox.Count - 1 do
      DBGrid.Columns[I].Visible := CheckListBox.Checked[I];
  finally
    DBGrid.Columns.EndUpdate;
  end;
end;