I'd like to build a robotic arm...

I second the need for an external power supply for the servos. Under zero load conditions, the servos will draw verry little current. However, as the load increases, the current draw will quickly increase past the max allowed by the arduino.
The way a servo works is by combining a dc motor and gear set with a potentiometer. It uses the potentiometer in a closed loop feedback so when you set the servo to a specific angle, the servo will hold at that angle. If you try to turn the output shaft, the servo will attempt to maintain its position by applying a voltage to the dc motor.