Let's say you have a list of Book elements (like here), each of which have a title, author and category fields. Now if on a page you want to show a filtered list of only the books from category Fiction, you can do this:
{% elementscontext category="Fiction" %}
<h2>Fiction books</h2>
<ul>
{% for fiction_book in elements %}
<li><b>{{ fiction_book.title }}</b> by {{ fiction_book.author }}</li>
{% endfor %}
</ul>
{% endelementscontext %}
This will give you only the books from category Fiction:
Fiction books
The Abilene Trail by Ralph Compton and Dusty Richards