That question has been answered by the guys at iFixit, who as usual, have been the first to tear apart and document the internal workings of the Apple TV. The answer: 8GB of NAND flash RAM made by Samsung. The iFixit team speculates that the RAM is most likely going to be used to cache incoming video streams, but it might also be used to temporarily hold apps that could run under iOS on the device.
More interesting news about the Apple TV is bound to come out in the next couple of days; stay tuned to TUAW for all of your Apple TV coverage.
Correction to original post: that's 8GB of onboard flash storage, 256MB of actual RAM. We apologize for the error.