There are many different types of microdata in existence, some have been around for longer than others, and some are easier to use than others.
The most commonly used and widely adopted came about when Google, Yahoo and Bing together chose to support the markup provided at www.schema.org - a common set of 'schemas' which provide website designers with a massive selection of contextual information that they can choose to provide to search engines.
Why use microdata?
Until fairly recently, microdata wasn't really used much so there wasn't much point in making the effort to include it. Search engines are, however, increasingly relying on and requiring contextual information in order to return the most relevant resources to the people searching. Ultimately, if their results are relevant, people will use their search engines more, therefore they make more revenue from their paid advertising.
To make sense of the vast amount of information on the web, search engines require contextual information - and semantic markup is a way of giving it to them, so that they can do more with the information you provide! Below you can see some examples where microdata has been pulled into search listings - author photos and information about how many people have them in their Google+ circles, star ratings, forthcoming event dates, time taken to bake a recipe (and calorie count!), and information about the duration of videos. This is just a small sample of the power you can leverage if you start using microdata on your website.