It seems Twitter is testing a new option called "Twitter Media," as the setting were appeared under Twitter's "Settings" menu. And then disappered. "This appears to indicate that inline image and video sharing is making its way to Twitter.com shortly. The option appears on my account, but checking the box does nothing so far."
Twitter says "We're constantly exploring features and settings. What you saw was a small test of a potential consumption setting for inline media. We show inline media on our own iPhone and Android apps."