How Servos Work
Based on these details of your question:
I just got a kit [...] continuous servos [...] plugged it into the
Combined with your "Arduino" tag, I'm betting that you are working with hobby (RC) servos modified for continuous rotation. Standard servos work by receiving a pulsed signal with a 20ms period (50Hz). Regular hobby servos will rotate to a specific angle based on the duty cycle (ON time) of the pulsed control signal. This on time can range from 500us to 2500us, but usually only a range of 1000us to 2000us is used so as to not damage the servo. The "neutral pulse" of 1500us will put the servo in the center position.
This Wikipedia article about servo control has a great picture regarding the pulsed control:
There are a few different ways that the servo works, but the most common type I've seen in use by hobbyists is an analog servo. As the motor turns, an internal potentiometer is adjusted creating a feedback path for the internal circuitry. The servo will continue to rotate until the potentiometer is at the expected position for the given pulse width.
There are numerous different ways of modifying a standard hobby servo for continuous rotation, so I won't go into that, but essentially, this feedback path is tampered with such the servo never thinks it is in the correct position when it gets a non "neutral" pulse. A mechanical stop on the internal gears is also removed. Once this is done, sending a non neutral pulse will cause the servo to rotate completely, with the speed of rotation dependent upon the pulse width.
When a non-modified servo is given a pulse, it will quickly rotate to the desired position and hold it as long as a pulse is being sent. It should be very difficult to manually turn the servo at this time, and doing so will cause the internal motor to hum as it draws excessive current trying to correct itself during this overload situation. If the servo is disabled (receiving no pulse) it can be manually manipulated with ease.
A modified servo will exhibit similar behavior when under too much of a load - it will hum loudly and draw excessive current. While your servo may not be overloaded, it is obviously exhibiting similar symptoms and is most likely defective. When being driven, manually turning the actuator or stopping it from turning in its desired direction/speed is not a good idea, so keep that in mind for your other servos.
When the defective servo tries to rotate, it is drawing so much current that the second servo cannot operate. That is why it worked fine once the defective servo was removed.