So basically as you can imagine from its name, low light camcorder is the one that allows you to film in the low light conditions. I have to say that even if you have professional equipment, not always you will want to use it to provide the lights. There are a lot of situations when you want to shoot some episodes in a totally natural lights. In this case you can't get away without a solid low light camcorder.
Another situation you might face with is when you are filming some situational episodes of your happy family. Not always you want to film on the daylight or with proper lights on in your house. It can happen somewhere outside in the evening or at night. If you are going to shoot it with a normal camcorder, then you are not going to see anything. If you are going to shoot with a in-built flash light that comes with a camcorder, it's not going to be as good spread light of high quality as it would be with a good low light camcorder.
What is the actual difference between a normal camcorder and a low light one is that the low light camcorder has the ability to pass through the higher volume of light. Just like some DSLR photo cameras and low light lenses do. You can also compare it with your vision. When you enter the dark room after being in the sun, you can't see pretty much anything. This how a regular camcorder behave in the dark environment. But after you spend few moments in the dark room, you start see the objects or even colours. This is how a low light camcorder acts.
The outcome you get is incredible! You are seeing a high quality picture and natural colours. Now the question is how to choose the best low light camcorder that would meet your needs. I've stumbled upon a solid read recently where the best low light camcorders on the market get reviewed. I'd recommend you to start off there.