Apple last week released for second- and third-generation Apple TVs, adding support for the new Up Next feature that debuted in iTunes 11, along with performance and stability improvements. However, there are a number of  updating over wired Ethernet connections. In some cases, the Apple TV may fail to boot after a failed update.
The solution is to unplug the Ethernet cable and update over Wi-Fi. That has worked for many people for whom the update wouldn’t install. However, if your install failed such that the Apple TV won’t boot at all, you can by unplugging the power and HDMI cables, and connecting it to your computer with a micro-USB cable (for a third-generation Apple TV, you’ll have to reconnect the power cable after this). Open iTunes, select the Apple TV from the Source list (located in the sidebar in iTunes 10 and from the Devices button in the upper-right corner in iTunes 11), and click Restore.
Of course, it may also just be worth holding off on the 5.1.1 update entirely if you don’t need the Up Next feature and aren’t experiencing any other problems that the update might fix. Apple will likely release either 5.1.2 or a new version of 5.1.1 shortly.