You can remove the paragraph tags, but it requires some code. Your best bet would be to leave it alone, and just use CSS to change how the P tag is displayed. So in your theme file:
<div class="cat_desc"><?php echo category_description(); ?></div>
and in your CSS:
div.cat_desc p { display:inline; }
If there's a block-level element before the P tag (such as an <h2> tag or something) then it'll still push it to the next line. So in that case, you could do:
<div class="cat_desc">
<h2><?php get_the_categry(); ?></h2>
<?php echo category_description(); ?>
</div>
and in your css:
div.cat_desc h2, div.cat_desc p { display:inline; }