Significance of Vf terminal in Li-Ion Battery
I am not sure about this particular battery, but I have seen two uses for third battery pin:


battery detection. For example, ISL9228 is a battery charger IC. Its datasheet http://www.intersil.com/content/dam/Intersil/documents/isl9/isl9228.pdf says:


  VF (Pin 7)
  
  VF is an input pin for the battery ID resistor connection. This pin
  has an internal 1000kΩ pull-up resistor. Thus a typical 20kΩ ID
  resistor will pull this pin to logic low state, indicating a valid
  battery connection. If the battery is removed, the VF pin will be
  pulled to a logic high state by the internal resistor, the charger
  will be disabled as a result, regardless of the status of the EN pin.
  The maximum ID resistor is 100kΩ.

Battery temperature monitoring. Smart Battery Specification http://sbs-forum.org/specs/sbdat110.pdf gives an example:


  As a required safety feature, the charger must NOT
  charge a battery when it senses the resistance between the Safety
  Signal pin and ground to be in the range between 425 and 3150 ohms. A
  NiMH battery which may use a 103AT thermistor as the source of the
  Safety Signal would enter this range if it got too hot; or the Safety
  Signal of a Li-ion battery may which use discrete resistors could be
  set to this range in an emergency condition.