How to display category specific post content on a page

Codex

Just take a look at the WordPress Template Hierarchy.

Templates

You’ll find out that WordPress has three different types of templates, that you can use:

A) For built in taxonomies: Category & Tag

B) For custom taxonomies.

The template engine will search for such templates when you request a category/tag/custom taxonomy archive page.

• taxonomy-{$taxonomy_slug}-{$term}.php
  • » taxonomy-{$taxonomy_slug}.php
  • » taxonomy.php
• category-{$slug}.php
  • » category-{$id}.php
  • » category.php
• tag-{$slug}.php
  • » tag-{$id}.php
  • » tag.php

Overview

^{The excellent diagramm by our man Chip Bennet.}