The tag for add images is
<img src=""> on the
srcattribute you need to write the url of the image you want (in your case
/images/logo.png) so, replacing the code you pasted
<h1><a href="<?php echo get_settings('home'); ?>"><img src="/images/logo.png"></a></h1>
Take into account that the path to the image you are using now is a relative one (relative to the document requiring the image) so you probably want to have the absolute url instead.