Sounds like you're using the default Kubrick theme. To get rid of the header text, from the Admin panel, go to Presentation - Theme Editor. On the right hand side is a list of files in the theme. You want to edit header.php.
Scroll down to the area (about 2/3 from the bottom) where you see
<div id="header">. About 3 lines down is the code:
<div class="description"><?php bloginfo('description'); ?></div>
This is the code that displays the description. To get rid of the description, comment out the line, using the HTML comment tags, as follows:
<!-- <div class="description"><?php bloginfo('description'); ?></div> -->
Click the Update File button and view the blog.