subtitle to the right of the logo

you can add this to your child-theme functions.php:

function kriesi_logo_addition($sub){
  $sub .= "<span class='logo-title logo-subtitle'>";
  $sub .= get_bloginfo( 'description', 'display' );
  $sub .= "</span>";
  return $sub;
}
add_filter('avf_logo_subtext', 'kriesi_logo_addition');

now the rest will be quick css work. Depends on your header setting and dimensions.
If you do not see it directly – it is placed below the header – you had to shift it then to the position you like
big advantage of that insertion – the subtext will follow a shrinking header behavior – because this is part of logo

if you look on top of this page here ( our forum ) you see kriesi logo with additional Text.
if you look to the DOM :

this might be done in a similar way – and because i do take the same classes – you can see how the board has set its css for it

add_filter('avf_logo_subtext', 'kriesi_logo_addition');
function kriesi_logo_addition($sub){
  $sub .= "<span class='logo-title'>";
  $sub .= get_bloginfo( 'name', 'display' );
  $sub .= "</span>";
  $sub .= "<span class='logo-title logo-subtitle'>";
  $sub .= get_bloginfo( 'description', 'display' );
  $sub .= "</span>";
  return $sub;
}

/*position logo text*/
#top .subtext{float:left; position: relative;}
#top .logo img{float:left;}
#top .logo, #top .logo a{overflow: visible;}
#top .logo-title{  
transition: 		opacity 0.4s ease-out;
-moz-transition: 	opacity 0.4s ease-out;
-webkit-transition: opacity 0.4s ease-out;
-o-transition: 		opacity 0.4s ease-out;
font-size: 12px; color: #000; position: absolute; left:7px; top:-7px; opacity: 1; white-space: nowrap; } 
#top .logo-subtitle{ color: #aaa; top:7px; }
#top .header-scrolled .logo-title{ opacity: 0; filter: alpha(opacity=0); }

@media only screen and (max-width: 989px) {
	.responsive #top .logo-title{ opacity: 0; filter: alpha(opacity=0); }
}