What is rich markup?
Rich markup on a page results in a rich search snippet on Google SERPs. According to GWT: Rich Snippets Guidelines
Rich snippets are designed to summarize the content of a page in a way that makes it even easier for users to understand what the page is about in our search results.
Rich markup can help with your Local SEO according to Mike Wilton's article. And it can be used to showcase a number of things on ecommerce websites such as mention by Joydeep Deb at another good SEP article on the matter.
The bottom line is that user site experience starts with a search results page (SERP). So the way your listing looks makes the first important impression. It should also be noted that rich snippets positively affect the click through rate from Google SERPs. For more examples of what you can use rich snippets for feel free to check an article by Craig Bradford and review these examples.
Does it affect rankings?
No, rich markup does not affect your rankings. Although there might have been strong correlation between sites using rich markup and higher rankings, it's likely that other factors on those page might have affected the rankings. Keep in mind, rich snippet affects the CTR and that's a much more important factor you should focus on this year than just rankings.
Adding rich markup to your pages
There's a number of ways to implement rich markup on your pages. Good news for WordPress-based site owners because Raven Tools team has developed a rich markup plugin to address the implementation. This plugin make rich markup implementation simple.
Just make sure you scan through these steps detailing the addition of rich snippets using this plugin described at Raven's Blog.
What if I don't run WordPress? Not a problem either. See this extension for Joomla. Or check this module if you run a Drupal-powered site. Refer to documentation at Schema.org and read an article by Eric Enge at Search Engine Land.
In either case, keep in mind that user experience (in at least 50-75% of cases) starts with SERPs and make sure that this is a good first impression. And be sure that rich snippets help users make their first step towards the purchase consideration simpler.