Edit in JSFiddle

function MyViewModel() {
    var self = this;
    self.places = ko.observableArray(['London', 'Paris', 'Tokyo']);

    // The current item will be passed as the first parameter, so we know which place to remove
    self.removePlace = function (place) {
        self.places.remove(place)
    }
}
ko.applyBindings(new MyViewModel());

<ul data-bind="foreach: places">
    <li> <span data-bind="text: $data"></span>

        <button data-bind="click: $parent.removePlace">Remove</button>
    </li>
</ul>