Each post in WP can be tagged and categorized. The posts can then be pulled from the database by various criteria - author, category, tag, date etc.
Read more here : http://codex.wordpress.org/Class_Reference/WP_Query
You could assign various columns on your homepage to display posts from different categories.
There are also different kinds of posts (post formats) such as image, video, quote etc. - which could all be displayed differently, depending on the theme (template).
Posts, post formats, categories, tags - all of these are a part of the standard WordPress install and are independent from the theme. The theme simply takes advantage of these features.