W3C stands for the "World Wide Web Consortium". The W3C was founded and is chaired by the original pioneer of the Internet - Tim Berners Lee.
The W3C sets the standards by which websites should be built. Here is their mission statement:
"To lead the World Wide Web to its full potential by developing protocols and guidelines that ensure long-term growth for the Web."
Building websites that adhere to the W3C guidelines is often much harder than building websites that don't. It is therefore usually more costly to do. The advantage is that you can be sure that your website will be more accessible to more people amongst many other benefits.