So they'll be a shorter version of this on the main site soon, but I can spell it out at greater length and more informally here. (I'm EFF's International Director, btw)
The short answer is that you're signing your support for a set of 13 principles on the application of human rights to communications surveillance ( see https://necessaryandproportionate.net/ ), that were worked out last year (pre-Snowden, actually) by a coalition of technologists, privacy activists, and legal scholars.
The long answer: We've been using this language to push the idea in international venues and among key lawmakers in various countries that mass surveillance (as well as a bunch of other practices conducted by the NSA and other spooks, including corruption of crypto standards and backdoors) is a violation of existing human rights standards.
This is important internationally because if the NSA gets away with its current behaviour, it'll establish a norm that such surveillance is okay for any government to conduct. We need to push back against that norm.
To do so, diplomats, policymakers and others need language and arguments to back that up.
The Principles give them that language in a familiar context (and we're working together to provide more detailed arguments and other legal guides). It has found favor among politicians, experts and other influential people I think partly because the smarter ones are genuinely worried that pervasive surveillance really could undermine their own societies -- they recognise what it could do in the wrong hands as much as anyone else.
In providing that leverage, it helps to convey that it's not just a bunch of domain experts that think forbidding mass surveillance is a bad idea, but that an increasingly large number of citizens find it abhorrent. That's what the signatures will do. It really makes a difference in this arena, because so few obscure technical documents have hundreds of thousands of supporters :)
I'd encourage anyone who wants to understand better how we're trying to get all governments, not just the US, to craft better surveillance legislation to read the full text of the principles at https://necessaryandproportionate.net/text You can also ask me questions at danny@eff.org . It's a long haul project, and we're conducting it alongside legal actions in the US and abroad, shoring up and disseminating crypto tools, and other non-policy defences. But it's pretty amazing to get unanimity with hundreds of privacy groups on some basic principles with which to start building proper, 21st century, surveillance law.