Need a little help with basic understanding of how categories work
Your code is only listing entries in the structure that are nested inside 2 parent entries. Try this:

{% for entry in craft.entries.section('structure').relatedTo(cat) %}

Also, your &lt;ul&gt; is inside your for loop, it should be:

&lt;ul&gt;
    {% for entry in craft.entries.section('structure').relatedTo(cat) %}`
    &lt;li&gt;{{ entry.title }}&lt;/li&gt;
    {% endfor%}
&lt;/ul&gt;