Edit in JSFiddle

function CharactersController($scope) {
    
    //  Add some characters to the scope.
    $scope.characters = [{
        name: "Fry",
        show: "Futurama"
    }, {
        name: "Homer",
        show: "The Simpsons"
    }, {
        name: "Sterling",
        show: "Archer"
    }, {
        name: "Kahn",
        show: "King of the Hill"
    }];
    
    //  A function to add a new character.
    $scope.addCharacter = function(name, show) {
        $scope.characters.push({name: name, show: show});
    };
    
    //  A function to remove a character.
    $scope.removeCharacter = function(character) {
        for(var i=0;i<$scope.characters.length;i++) {
            if($scope.characters[i] !== character) {
                continue;
            }
            $scope.characters.splice(i, 1);
            break;
        }
    };    
}

<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.2.0/angular.min.js"></script>
<div ng-app ng-controller="CharactersController">
    <table>
        <thead>
            <tr>
                <th>Name</th>
                <th>Show</th>
            </tr>
        </thead>
        <tbody>
            <tr ng-repeat="character in characters">
                <td>{{character.name}}</td>
                <td>{{character.show}}</td>
                <td><a href ng-click="removeCharacter(character)">Remove</a></td>
            </tr>
            <tr>
                <td><input type="text" ng-model="name"></input></td>
                <td><input type="text" ng-model="show"></input></td>
                <td><a href ng-click="addCharacter(name, show)">Add</a></td>
            </tr>
        </tbody>
    </table>
</div>