Edit in JSFiddle

$(document).ready(function() {
    var viewModel = function() {

        var country = function() {
            this.key = ko.observable();
            this.cname = ko.observable();
        };

        var state = function() {
            this.countryKey = ko.observable();
            this.sname = ko.observable();
        };

        var countries = ko.observableArray([]);
        var states = ko.observableArray([]);

        var load = function() {
            // add countries
            countries.push(new country().key(1).cname("USA"));
            countries.push(new country().key(2).cname("India"));

            // add states
            states.push(new state().countryKey(1).sname("New Jersey"));
            states.push(new state().countryKey(1).sname("New York"));
            states.push(new state().countryKey(1).sname("Ohio"));
            states.push(new state().countryKey(1).sname("Kentucky"));

            states.push(new state().countryKey(2).sname("MP"));
            states.push(new state().countryKey(2).sname("UP"));
            states.push(new state().countryKey(2).sname("Maharashtra"));
        };

        // keep track of selected country
        var selectedCountry = ko.observable("");
        var selectedState = ko.observable("");

        var selectedCountryName = ko.computed(function() {
            var cntry = selectedCountry();

            if (cntry) {
                return cntry.cname();
            }

            return "";
        });

        var selectedStateName = ko.computed(function() {
            var st = selectedState();
            if (st) {
                return st.sname() + " , ";
            }
            return "";
        });

        // change state selection based on country selection
        var selectedStates = ko.dependentObservable(function() {
            var cntry = selectedCountry();
            var cntryKey;

            if (cntry) {
                cntryKey = cntry.key();
                return ko.utils.arrayFilter(states(), function(item) {
                    return item.countryKey() === cntryKey;
                });
            }

            return [];
        });

        // public members
        return {
            countries: countries,
            states: states,
            load: load,
            selectedCountry: selectedCountry,
            selectedStates: selectedStates,
            selectedCountryName: selectedCountryName,
            selectedState: selectedState,
            selectedStateName: selectedStateName
        };
    }();

    viewModel.load();
    ko.applyBindings(viewModel);
});

<select data-bind="options:countries, optionsText : 'cname', value:selectedCountry, optionsCaption:'Select...'"></select>
<select data-bind="options:selectedStates, optionsText : 'sname', value:selectedState, optionsCaption:'Select...'"></select> <br/><br/>
<span data-bind="text:selectedStateName"></span><span data-bind="text:selectedCountryName"></span>