The potential for such a phishing scam was first discovered by a Finnish developer, who realized that it's fairly simple to poach info from people by planting rogue text boxes on a particular target page. That's because many browsers' autofill systems work by automatically plugging in pertinent stored info -- your mailing address, phone numbers, credit cards, etc. -- into blank text boxes in an online form. By attempting the scheme himself, he found that would-be scammers could simply add additional "hidden" boxes to the page, and trick people into giving away more info than they intended to.
Affected browsers include biggies like Chrome, Safari, and Opera, as well as extensions like the password manager/form filler LastPass, which is perhaps an even more obvious target. So, if you're currently using any of these, it'd be wise to head to your Preference menu and temporarily disable the autofill feature until a security patch is pushed out.