The standby mode essentially disconnects the outputs to the speakers and leave the amplifiers on. In case of a power spike the speakers will be protected.
The amplifier stays on and keeps all of the silicon devices warm. They perform optimally at a specific temperature, which can take 24 hours to achieve from a cold start. You can let your ear decide if the power to keep the amp warm all the time is worth it
I typically keep my system on unless I will be out of town for a day or two. Compared to other power appliances, it is pretty minimal consumption!