NPN transistor switch with load at emitter pin
If C2 were a larger value such as 10nF, it being in parallel with R2 to a transistor base, would be called a speed-up capacitor.
Generally this is done to &quot;speed-up&quot; the base current transition. Remember, capacitors resist a change in voltage. Without the capacitor, R2 completely determines how much current goes into the base.  And transistors have parasitic capacitance to the base, so R2 is also charging and discharging this capacitance. That is what limits transition speed, and why a speed-up capacitor is sometimes used.
The bigger the C, the harder it will &quot;push&quot; the base at the moment of voltage change, overcoming it's parasitic capacitances, resulting in faster switching.
As for figure 1, that must be an error. Q1 should be a PNP type (NPN will not work correctly.)