W3C is compliance to standards like xhtml, html5, css and previous versions.
Semantic mark-up is extensions to these standards that let you add more meaning to your content.
A simple example is you can add mark-up to your contact page to tell search engines what represents your name, address, phone number, mobile...
This sort of mark-up can cover things like products, testimonials, business details, people etc.
The benefit is Google may gather marked-up data and use it to make you look better in the search results. You've probably seen product images, rating stars, breadcrumbs and authors in search results. These are often added because of the semantic mark-up on the page in question.
And it's not just Google. Facebook supports the open graph protocol that lets you define how your page is displayed in Facebook.
On running applications on WP. Anything is possible and there are a lot of WP developers out there to solve things. It's more to do with how your applications are coded.