Ok, I assume viewing the image you know how to edit templates... so, lets do this!
HTML
Go to header template
You will see this:
<div id="header">
<div class="wrapper">
<div class="logo"><div class="logo2"><i class="fa fa-cube fa-fw"></i></div> Square</div>
<div class="menu">
<ul>
<li><a href="{$mybb->settings['bburl']}/index.php"><i class="fa fa-comments fa-2x"></i><br />Index</a></li>
<li><a href="{$mybb->settings['bburl']}/search.php"><i class="fa fa-search fa-2x"></i><br />Search</a></li>
<li><a href="{$mybb->settings['bburl']}/memberlist.php"><i class="fa fa-users fa-2x"></i><br />Members</a></li>
<li><a href="{$mybb->settings['bburl']}/calendar.php"><i class="fa fa-calendar-o fa-2x"></i><br />Calendar</a></li>
<li><a href="{$mybb->settings['bburl']}/misc.php?action=help"><i class="fa fa-question-circle fa-2x"></i><br />Help</a></li>
</ul>
</div>
</div>
</div>
Then, below the "wrapper", put this:
<div class="banner">Your banner</div>
"Your banner" is the image or the thing you want to display there.
CSS
Now, go to square.css
search the ID "Header" (#header)
#header {
background: #005ea7;
height: 200px;
}
You need to change the height, actually have a 200px, so, do a quick math with the 200px and the total height of your image or thing and put the result there (Example: 400px)
Now, go to the end of square.css and add this:
.banner {
margin: 0 auto;
padding: 10px 0;
}
That code simply add a 10px padding (10px space from the top) and the margin center the element in the header.
Now the only thing you need to do is put your image or ad inside the banner <div> tag and that's all!