A twibbon is a promotional banner - like a ribbon - on Twitter sites. It's used to show support for causes.
More than 9,300 people (at this point) are using a "We love the NHS" twibbon. According to the download site, that's supposed to show that:
"We're proud to support our NHS! Show the world (and the American right) that we've got a great healthcare system, with the best doctors, nurses, administrators et all in the land!"
Here are some of those twibbon users from the twibbon.com site.