Assuming standard HTML structure like so:
<h3><span>Section 1</span></h3>
<div>
<p>
Mauris mauris ante, blandit et, ultrices a, suscipit eget, quam. Integer
ut neque. Vivamus nisi metus, molestie vel, gravida in, condimentum sit
amet, nunc. Nam a nibh. Donec suscipit eros. Nam mi. Proin viverra leo ut
odio. Curabitur malesuada. Vestibulum a velit eu ante scelerisque vulputate.
</p>
</div>
And assuming that you're targeting H3 elements individually, you'd use:
$(this).next('div');
If you need to get that div from the span with the class you've matched, it would be:
$(this).parent('h3').next('div');