The shunt electrolytic capacitor, C1, stores a local resevoir of power for the microphone being phantom powered, which helps to isolate its 48V power from the rest of the mics connected to the same supply. This is called "decoupling" or "power supply rejection", and generally enhances circuit performance. Adding a series resistor, R1, can greatly increase decoupling by forming a low-pass filter. This filter has a cutoff frequency very close to 0Hz, such that (in theory) only DC passes and none of the AC noise.

These two components are optional. In their absence, R1 becomes a short and C1 is left open. While there should be no reason to leave out C1, R1 can decrease the voltage of the phantom power supply, possibly compromising the performance of some microphones. You can calculate this voltage drop using Ohm's Law to see if it will be harmful. For example, if R1 is 1kΩ and the mic is drawing 5mA of current, then there's a loss of 5VDC. 48 - 5V = 43V, which shouldn't be a problem for most mics, but still something to consider.