Why use decoupling capacitor with Servo S2309S and how does it work?
The wire connection going to the servo power input will act as a small resistance and inductance, if you draw a large current quickly (as starting up a motor does) there could be a voltage spike, (usually small, but possibly enough to cause noise on the line).  Adding a decoupling capacitor allows some of the instantaneous current to come from the capacitor instead of the power line, thus keeping the power line glitch free.  

Without the capacitor you may not see any difference in the movement of the servo.  But if you have a scope on the servo's input wire you may see a voltage spike as the servo starts up.