In layman's terms, it is a way for certain markup to have a reserved meaning for the search engines to use do determine what the page is about.
For instance, suppose you are a small business who manufacturers brake products for cars. If you were to build your page about this product, you would try to craft the keyword targeting so that Google can figure out that this page is about your brake shoes. Now as you might imagine, there are thousands of types of brake pads for every manufacturer of auto.
Search engines needed a way for people to tell them exactly what the page is about, so microdata was developed.
If you use any type of microdata, you will markup the page so that the search engine can look in a certain place and see exactly what something is instead of analyzing the age and trying to tell.
With Microdata, you tell the search engines that your product is brake pads, but you can also tell them model numbers and such. So the search engine knows that the page is about a specific brake pad by looking at the markup.
You an define all sorts of things with microdata. My bailiwick is Local SEO so I will give you an example of where microdata, (Schema is a form of microdata) is beneficial. I have a customer who has 4 phone numbers, a toll free line, two business lines (land line and cell), and a fax number on their website.
With schema markup, I can tell goggle that the main business land line is the official phone number for the business, eliminating any confusion in the algo caused by multiple phone numbers on the page, which helps me maintain consistency in my NAP.
If you use schema/other forms of microdata you will be able to optimize the page to a deeper level with a method developed specifically for that purpose.
This is tremendously helpful for sites that have similar products.
With schema, you can make a page not only about blue widgets, but you can tell the search engines that this page is about a specific model of this blue widget is the XL500 with the titanium rollers and stainlesss steel chain in size 4 for use with the Dagon mounting systems.
Or that this location is the one off Hiway 301, not the one on Route 4.