Edit in JSFiddle

var viewModel = {
    items: ko.observableArray([{
        itemName: 'Choice 1'
    }, {
        itemName: 'Choice 2'
    }]),
    chosenItems: ko.observableArray()
};
ko.applyBindings(viewModel);

<!-- ko foreach: items -->
<input type="checkbox" data-bind="checkedValue: $data, checked: $root.chosenItems" /> <span data-bind="text: itemName"></span>
<!-- /ko -->