What does this circuit on my battery do?
This would be the battery protection circuit of the Li-Po battery. It prevents over-current over-voltage and under-voltage as a minimum in most Li-Po battery systems. This circuit and its parameters are set by the manufacturer, for the particular Li-Po it is meant to protect. Generally it is not a good idea to tinker around with this as it could render the battery potentially insecure and dangerous. You would need to contact the manufacturer to obtain the details of this circuit you request as they are generally not made public for a good reason. However the silicon device with the marking VC55 should be easy enough to find I guess if you look hard enough for it. Then you may better understand how the circuit works. Having said that, the 3 pin on such a system may be allocated to a thermistance output for measuring the battery temperature directly. Those that only provide two pins don't have the thermistor installed or available.
Hope this makes sense.
Regards,
citizen