Edit in JSFiddle

Vue.component('my-child', {
	template: [
  	'<div class="child">',
  	'<h2>Child Component</h2>',
    '<input type="text" v-model="childMessage" v-on:input="onInput"></input>',
    '<button @click="apply">apply</button>',
    '<p>{{ parentMessage }}</p>',
    '<p>{{ value }}</p>',
    '</div>'
  ].join(''),
  props: ['parentMessage', 'value'],
  data () {
  	return {
    	childMessage: ''
    }
  },
  methods: {
  	apply () {
    	this.$emit('apply-from-child', this.childMessage)
    },
    onInput (e) {
    	this.$emit('input', e.target.value)
    }
  }
})

const app = new Vue({
	el: '#app',
  data () {
  	return {
    	messageFromChild: 'message from child',
      messageVModel: 'message v-model'
    }
  },
  methods: {
	  apply (value) {
    	this.messageFromChild = value
    }
  }
})

<div id="app">
  <div class="parent">
    <h2>Parent</h2>
    <p>{{ messageFromChild }}</p>
    <p>{{ messageVModel }}</p>
  </div>
  <my-child parent-message="literal-from-parent" v-on:apply-from-child="apply" v-model="messageVModel"></my-child>
</div>