No HDMI...
First off, not many people actually use HDMI with a tablet. Apple has AirPlay so you can put the screen on a TV with a AppleTV box. Wireless for $99, more convenient. Now, if you REALLY, REALLY need HDMI output to connect a HDMI cable, then you can buy an adapter to connect to the Lightning port and do it that way. The cost is $49. http://store.apple.com/us/product/MD826ZM/A/lightning-digital-av-adapter
So, it does do HDMI output, it just requires a minimal cost for an adapter. But the majority of iPad users don't connect with HDMI. For convenience, wireless connection with an AppleTV is preferred for people in the Education and Business market.