Power Supply Rejection Ratio for Battery Powered Systems
The reason why PSR is important even in battery supplied devices is that one can (and usually) have several different kinds of circuits supplied from the same battery in the same device. Due to internal resistance of the battery, changes in the current consumption of the one part of the device will be seen as voltage variation for all the circuitry supplied by thereof. 

One dramatic example is GSM phone, where power amplifier for transmitter will consume significant amount of current (amps range) every time the frame is transmitted with almost no current consumption in between frames. Assuming* 0.5 Ohm internal resistance and 1A consumption that means 500mV voltage variation repeating several hundreds times a second.

*) those are example numbers, too lazy to check actual GSM numbers