Replace with below code.

HTML

<asp:DropDownList ID="ddlCountries" runat="server" multiple="multiple" CssClass="multiselect">
    <asp:ListItem Text="Argentina" Value="Argentina"></asp:ListItem>
    <asp:ListItem Text="Austria" Value="Austria"></asp:ListItem>
    <asp:ListItem Text="Belgium" Value="Belgium"></asp:ListItem>
    <asp:ListItem Text="Brazil" Value="Brazil"></asp:ListItem>
    <asp:ListItem Text="Canada" Value="Canada"></asp:ListItem>
</asp:DropDownList>
<asp:HiddenField ID="hfSelected" runat="server" />
<asp:Button Text="Filter" runat="server" OnClick="Country_Changed" />
<hr />
<asp:TextBox ID="txtDetails" runat="server"></asp:TextBox>
<div>
    <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
    <link rel="stylesheet" type="text/css" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.0.3/css/bootstrap.min.css" />
    <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.0.3/js/bootstrap.min.js"></script>
    <script src="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-multiselect/0.9.13/js/bootstrap-multiselect.js"></script>
    <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-multiselect/0.9.13/css/bootstrap-multiselect.css">
    <script type="text/javascript">
        $(function () {
            $('[id*=ddlCountries]').multiselect({ includeSelectAllOption: true });
            $('[id*=ddlCountries]').on('change', function () {
                $('#<%=hfSelected.ClientID%>').val($(this).val());
            });
        });
    </script>
</div>