navbar fixed top does not work

Even though, a fixed top navbar has been added, the div which is under the navbar starts from the very top of the page. The top part is under the nav bar

HTML

<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap-theme.min.css">
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
<body>

  <!-- Fixed navbar -->
  <nav class="navbar navbar-inverse navbar-fixed-top">
    <div class="container">
      <div class="navbar-header">
        <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false" aria-controls="navbar">
          <span class="sr-only">Toggle navigation</span>
          <span class="icon-bar"></span>
          <span class="icon-bar"></span>
          <span class="icon-bar"></span>
        </button>
        <a class="navbar-brand" href="#">Bootstrap theme</a>
      </div>
      <div id="navbar" class="navbar-collapse collapse">
        <ul class="nav navbar-nav">
          <li class="active"><a href="#">Home</a></li>
          <li><a href="#about">About</a></li>
          <li><a href="#contact">Contact</a></li>
          <li class="dropdown">
            <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-haspopup="true" aria-expanded="false">Dropdown <span class="caret"></span></a>
            <ul class="dropdown-menu">
              <li><a href="#">Action</a></li>
              <li><a href="#">Another action</a></li>
              <li><a href="#">Something else here</a></li>
              <li role="separator" class="divider"></li>
              <li class="dropdown-header">Nav header</li>
              <li><a href="#">Separated link</a></li>
              <li><a href="#">One more separated link</a></li>
            </ul>
          </li>
        </ul>
      </div>
      <!--/.nav-collapse -->
    </div>
  </nav>

  <div class="container theme-showcase" role="main">

    <!-- Main jumbotron for a primary marketing message or call to action -->
   ...