What is the purpose of this resistor between BJT Base and Emitter?
That resistor speeds up turnoff and increases maximum allowed collector circuit voltage.

The turnoff speeding is based on the fact that the charge which is stored to the BE junction is dissipated in resistor R2. The effect is substantial in pulse circuits.

There's some leakage from C to B and it can cause substantial unwanted base current at high operating voltages. R2 sinks that leakage. The allowed max voltages in datasheets are often specified with R2 inserted.

I guess your R2=100kOhm is randomly selected. Practical R2 is often 100...1000x smaller.

ADD a simulation to demonstrate the effect to turn-off:

Here 5V 500kHz square wave (V1, red) drives a switching transistor 2N3904. The design is quite bad, the turn-on at the rising edge of V1 is slow and the turn-off at the falling edge of V1 is even slower due the stored charge in the BE junction:



Turn-on becomes faster when R1 is smaller, but the turn-off gets huge 400ns extra delay. That delay is called "storage time" and a small one can be seen already in the previous image:



Inserting R2 reduces the delay, but also degrades the turn-on speed:



R2 isn't perfect fix, but its better than nothing. 
The next is not asked, but it can be interesting:

Good performance is achieved with clamping diode and speeding capacitor:



The transistor sinks its excessive base current via D1 and the capacitor C1 gives a boost during both slopes of V1. D1 must be a low voltage drop type such as Germanium or Schottky diode, 1N4148 is useless. Here the used type is Schottky diode BAS81.