With the Stamina Mode on, your apps will not sync, check for notifications or incoming messages when the screen is off. Usually, those activities can munch on your battery, even with the phone in your pocket and the screen off. Stamina Mode also blocks data traffic and prevents it from waking up your phone. You will still receive calls, SMS messages and MMS notifications. Alarms will still ring, the native calendar app will work, and the LED light will only work to inform you about a low battery.
According to a tweet from tipster @Ricciolo1, once the Sony Xperia Z5, Sony Xperia Z5 Compact and Sony Xperia Z5 Premium are updated to Android 6.0, the Stamina Mode will be improved, making the Batteries "Real Champions." A 2900mAh juicer is inside the Xperia Z5, and a 2700mAh cell powers the Xperia Z5 Compact. A large capacity 3430mAh juicer powers the Xperia Z5 Premium. Sony says that the Xperia Z5 models can run for as long as two-days between charges.
source: @Ricciolo1 via AndroidWorld.it (translated)