This should be pretty straightforward. The post template you're using has author information hard-coded into it, so unless you want to duplicate some information you'll need to comment the code you've shown above out. This is basically what FAQ 5 is saying ...
I've installed and configured WP Biographia and now I see not one but two differing Biography Boxes; what's going on?
There's probably one of two things going on here. Firstly, you've already got another plugin that makes a Biography Box installed and active and this plugin, as well as WP Biographia, are doing their job properly. Secondly, the theme you're using hard codes a Biography Box into the theme templates. Both the TwentyTen and TwentyEleven themes supplied as part of a standard WordPress install do this.
You can either delete the code, or comment it out, along the lines of
<div id="post-author" class="clearfix">
<?php echo get_avatar( get_the_author_meta( 'user_email' ), apply_filters( 'platformbase_author_bio_avatar_size', 50 ) ); ?>
</div><!-- END author-avatar -->
<?php the_author_meta('description'); ?>
</div><!-- END author-description -->
</div><!-- END post-author -->
[Moderator Note: Please post code or markup snippets between backticks or use the code button.]
Then simply ensure your author (or author's) profile(s) have biographical information set in them and ensure that "Display On Individual Posts" is checked in WP Biographia's settings and options and you should be good to go.