The Esplora was not really designed for battery power. In the last two weeks I have used an Energizer "cell phone" backup battery into the USB port.
The more elegant solution is using a rechargeable LiPo battery. But this will not put out the 5 volts the Esplora needs. This is where an Adafruit Mintyboost works well to boost the 3.6 volts from the battery circuit boosts to 5 volts.
To feed the voltage in, I put it into the Tinkerkit output pins rather than the USB to create a lower profile and free the port for programming. Be careful not to have both connected at the same time.
Full details on how this was done are at The 21st Century Digital Home: LiPo powered Arduino Esplora Game Platform.
The project also adds an XBee radio that communicates via the two Tinkerkit digital pins which map to Arduino IDE digital pins 3 and 11. The only two free pins to play around with if you use a display.
