You can achieve this by adding new array to your vm for storing selected rows. Bind it to checkboxes using checked
binding:
function ViewModel() {
var self = this;
self.items = ko.observableArray(["One", "Two", "Three"]);
self.selectedItems = ko.observableArray();
self.deleteSelected = function () {
self.items.removeAll(self.selectedItems());
self.selectedItems.removeAll();
}
}
ko.applyBindings(new ViewModel());
<div data-bind="foreach: items">
<input type="checkbox" data-bind="value: $data, checked: $parent.selectedItems" />
<span data-bind="text: $data"></span>
<br/>
</div>
<input type="button" value="Remove Selected" data-bind="click: deleteSelected" />
Here is an example: http://jsfiddle.net/zvFnW/