Understanding balancing resistor in bipolar op amp
Is the "input bias current" the current generated from external power
  source or some unwanted current resulted from within the op amp
  circuitry when the op amp is powered?


The op-amp bias current is that small current that is needed by the op-amp's inputs to properly operate the device. This isn't always equal for both inputs and pretty much all data sheets refer to the difference in input bias currents as input offset current. That offset is unknown (without measurement) and may also change over time hence, using resistors to try and cancel offset current is not effective.

So you might have an input bias current specification of 100 nA and an input offset current specified as 10 nA. This might mean the true bias currents into the inputs are: -


+110 nA for one input
+90 nA for the other input


Equal value resistances in both input circuits will cancel the bias current but the offset current is still an unknown and cannot be easily reduced because we don't know what it is.

So the effect of input resistors causes both inputs to be slightly raised or lowered by the same amount when there is exactly equal bias currents and, this means that there is no extra offset voltage at the inputs that leads to the same error as what is called input offset voltage (another parameter in the data sheet for all op-amps).