There are a couple of reasons why modern HDTVs take time to turn on and show a picture (compared to old CRT & LCD TVs):
Modern HDTVs are more like computers than simple electrical / electronic devices. They have processors, random access memory and reprogrammable flash memory which holds a small embedded operating system (firmware / software). Turning on a HDTV is just like booting up the operating system (e.g. Windows) on your computer.
Newer Energy Star guidelines require Consumer Electronics manufacturers to maintain extremely low power consumption when a device is in stand-by mode to save electricity to reduce our carbon footprint. This forces HDTVs to do a complete boot up when turned on from stand-by.