It's a sort of micropayment service: You sign up and distribute a fixed amount of money per month (I.E. 10€). Everytime you click on a flattr-button (Which seem to shop up on german blogs only, in my experience), they will get a share. At the end of the month, your fixed amount divided by the number of shares is payed out to the sites.
There are some implementation details which results into calling themselves a 'social payment service'.
Which is worth pointing out - it is not a social payment service, it is a social donation service, since you get to view the content whether you pay or not.
There wouldn't be much difference, but taking donations is only a small part of what paypal does. You can donate money with a credit card, but that is not what it is mostely used for.
Flattr on the other hand, can only be used for donations, which means that it has little, if any value.
Flattr strangely seems to have taken off in Germany fairly quickly. And it seems to work. If you are a popular blog you already (with Flattr still being invite only until very recently) seem to be able to make between a few hundred and maybe a thousand Euro per month.
Another area where it may be taking off is Free and Open Source Software. See http://raphaelhertzog.com/flattr-foss/ ; dpkg is currently in the top 5 most flattrd things.
