YOu can do this with many different ways.
One way is to use display:flex; together with align-items:center. 
See below
/* Latest compiled and minified CSS included as External Resource*/
/* Optional theme */
@import url('//netdna.bootstrapcdn.com/bootstrap/3.0.0/css/bootstrap-theme.min.css');
.app-header{
  height: 50px;
  background: #000;
  color: #fff;
  display:flex;
  align-items:center;
  flex-wrap:wrap;
}
.container {
  width:100%;
}
.v-center{
  
}
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/css/bootstrap.min.css" rel="stylesheet"/>
<div class="app-header">
  <div class="container clearfix">
    <div class="pull-right v-center">
      Hello World
    </div>
  </div>
  
</div>
 
 
That would be a responsive solution meaning that no matter the height of the header, the text will be vertically aligned in the center of it.
Another solution would be to set the line-height of the v-center equal to your header height, in your case .v-center { line-height:50px}