Hello, I thought I would add to the answers already given with respect to the heart in particular. As already alluded to in a previous answer, the intrinsic rate of the SA node (which controls how fast the heart beats) is around 100bpm. Now to bring that down to our normal resting heart rate of around 70bpm, a tiny electrical pulse is sent from the brain to the heart at regular intervals (I'm trying to keep this simple to help understanding) via the Vagus nerve. This electrical pulse does not contain any information in itself, it is just either on or off, much like the electrical pulses sent to muscles to make them contract. You're not 'telling' the muscles to contract, you're just sending electrical pulses that make them contract, and so to make the muscle relax, you simply send less electrical pulses. So with that in mind, if the electrical pulses to the heart become even more frequent, the heart rate would go even lower than 70bpm because more electrical stimulation via the Vagus nerve results in more parasympathetic activity.
So, doing the opposite to the above, if we send less electrical pulses via the Vagus nerve to the heart's SA node it will speed up. If no electrical pulses were sent at all, the heart rate would rise back to 100bpm (the intrinsic rate of the SA node). Hopefully this makes sense so far.
Ok, so what if we only had this one nerve sending electrical pulses to the heart? Well, by taking in what we now know from above, the maximum rate the heart can now attain is only 100bpm. Something else is needed to send an electrical pulse to the SA node to get it to fire faster. We can't use the Vagus nerve because if we stimulate that, it will only serve to slow the heart down again. We need another nerve that, when stimulated, makes the heart speed up beyond 100bpm, this is where the sympathetic nerves step in. An increase in electrical activity from the sympathetic side causes the heart to beat above the 100bpm 'intrinsic' rate in order to meet demand.
This is a very simplistic way of how all this works as in reality there is always a balance between parasympathetic and sympathetic activity to enable the heart to quickly react to the requirements of the body.
Hope this helps in addition to the answers you have already got.