The Web Standards Project, or WaSP*, is a sort of lobbying group. Rather than focusing on politicians, they apply pressure to the manufacturers of web browsers, trying to convince them to produce software in line with the standards outlined by the World Wide Web Consortium (W3C).
WaSP was started in 1998 as a reaction to the increasing mess developers were making of their markup, CSS, and script, lacking a cohesive standard that worked in all available web browsers. (If you look at their archived site from that time**, you will probably be able to tell that Jeffrey Zeldman had a hand in this.) Their site was one of the first to talk about web design as anything more than a means to an end and to take the standards seriously.
It's not really exaggeration to say that WaSP is leading the somewhat cultish group of web designers who are embracing this change. This movement also venerates CSS Zen Garden, IE7, and A List Apart. Not suprisingly, both Dave Shea and Dean Edwards are WaSP members. Zeldman is no longer an active member, but, as mentioned, was part of this from the beginning.
Besides a lot of rhetoric, links, and relentless bullying of non-complying browser makers (which, don't get me wrong, have all been very helpful) the most useful things WaSP has offered up are the original Acid and Acid2 Tests. These are rendering tests that demonstrate whether a given browser is in or out of compliance with the W3C standards.
WaSP's statements seem to imply very clearly that the group will stick around until they've shifted the perspective of every web designer and everyone in a position to bankroll a website. That could be a long time, but more power to 'em.
* No, there's no 'a' in there, you're absolutely correct.