Panic Software, purveyor of Mac OS X applications, was curious why Apple's $49 Lightning Digital AV adapter wasn't performing very well. The picture quality was lacking, displaying odd video artifacts and failing to output full 1080p video. So Panic cracked open the case, and what should it find... but a tiny ARM computer chip inside. It's got an Apple logo on top, and markings indicate it might have 256MB of memory within.
Why does the adapter need a processor, though? Panic Software's theory is that the device actually delivers video via AirPlay streaming. Your iOS device would compress the video, then the adapter would decompress it and deliver it to an HDMI-equipped TV. The video artifacting, a common issue with video processed that way, seems to support the theory, as does the lag some users are reporting. We don't have an adapter handy to test for ourselves, but we've reached out to Apple to ask how the adapter works, and hope to hear back in future.
Update: Apple hasn't responded, but a commenter claiming to be an anonymous Apple employee has: they claim the device doesn't use AirPlay, but does indeed decode H.264 video sent over the Lightning cable using the ARM chip. They also claim that quality of the stream may actually improve over time, as Apple releases software updates. It sounds plausible, but again, it's an anonymous rumor.