Edit in JSFiddle

<!-- Main Div Holding our Application Data -->
<div class="container" id="todo">
  <!-- Panel for holding our input -->
  <section class="panel">

    <input type="checkbox" id="mark-all">
    <input type="text" placeholder="What do you need to do?" autofocus class="text-input" v-model="newTask" v-on:keyup.enter="addTask">
    <button v-on:click="clearList">Clear List</button>

  </section>

  <!-- Unordered list for holding our todo items -->
  <ul class="list">

    <li v-for="task in taskList">

      <input type="checkbox" class="checkbox" v-model="task.checked">

      <label for="checkbox">{{ task.text }}</label>

      <button class="delete" v-on:click="removeTask(task)">X</button>

    </li>

  </ul>

  <!-- This stringifies the contents of the data object and displays it on the page -->
  <pre>{{ $data }}</pre>

</div>

//Create a new Vue instance
new Vue({

  //Bind this Vue instance to our container div with an ID of todo
  el: "#todo",

  //This is where the data for our application will be held
  data: {
    newTask: "",
    taskList: []
  },

  //This is where we will register the methods we want to use in our application
  methods: {

    addTask: function() {
      //trim() is used to remove whitespace from both ends of a string
      var task = this.newTask.trim();
      //if task is not an empty string
      if (task) {
        //Push an object containing the task to the taskList array
        this.taskList.push({
          text: task,
          checked: false
        });
        //Reset newTask to an empty string so the input field is cleared
        this.newTask = "";
      }
    },

    removeTask: function(task) {
      var index = this.taskList.indexOf(task);
      this.taskList.splice(index, 1);
    },

    clearList: function() {
			//Setting taskList to an empty array clears the whole list
      this.taskList = [];
    }
  }
});

/* Relevant resets */


/* Reset the default browser styles on list items */

ul,
li {
  margin: 0;
  padding: 0;
  border: 0;
}


/* Global Styles */

body {
  line-height: 1;
  font-family: "Lato", sans-serif;
  background-color: #EFF1F2;
}

.container {
  width: 70%;
  margin: 1em auto 3em;
  border: 1px solid #efefef;
}

.panel,
li {
  /* Use flexbox */
  display: flex;
  /* Center everything inside .panel and li vertically */
  align-items: center;
  /* Distribute space evenly between the contents*/
  justify-content: space-between;
  list-style-type: none;
  padding: 10px;
  border-bottom: 1px solid #efefef;
  background-color: #E7E8EB;
}

.text-input {
  border: 1px solid #dedede;
  padding-left: 10px;
  width: 70%;
  height: 35px;
  color: #555;
}

button {
  color: #555;
  background-color: #FFFFFF;
  border: 1px solid #bbb;
  outline: 0;
  width: 100px;
  height: 38px;
  cursor: pointer;
  font-size: 12px;
}


/* Task  area */

.list li {
  background-color: #3465A4;
}

.list li .delete {
  background-color: transparent;
  border: 1px solid #3465A4;
  color: #ddd;
  /* Hide the delete button by default*/
  visibility: hidden;
  font-size: 20px;
  font-weight: bold;
}

.list li:hover > .delete {
  /* Show the delete button when hovering over each list item */
  visibility: visible;
}

.list label {
  padding-right: 10px;
  display: inline-block;
  width: 70%;
  font-size: 18px;
  line-height: 24px;
  color: #fcfcfc;
  z-index: 2;
  overflow: hidden;
}

.list li.done label {
  color: #d9d9d9;
  text-decoration: line-through;
}


/* Media Queries */

@media screen and (max-width: 768px) {
  .container {
    width: 90%;
    max-width: 90%;
  }
  button {
    width: 80px;
  }
}