Magic exists in the world of the Wheel of Time and it plays a huge part in the story. Here's how the system works in non-spoiler terms.

Level 1#

We'll first tell you how it works in plain English, using an analogy. As with all analogies, it's not perfect, but it will get you a basic understanding.

1. Imagine that you have a task to do. Let's say it's to grind some flour. You need a water mill for that, so you make one. But for that mill to work, you'll need water, which turns the wheel and then the mill converts the power of the water into the motion of the grinding wheel.
2. Lucky for you, you know of a source for water. A pond is nearby. Wait, it's a lake. Nope, it's an ocean.
3. Now you just need to use your trusty shovel and cut a channel from the ocean to your mill for the water to flow through. That channel has to be just the right size, though. Too small and it won't turn the mill wheel. Too large and you'll have a river running through, destroying your mill and maybe even your town.
4. Luckily, there's bunch of trained professionals that can help you, if they find you in time. They can't cut the channel for you but they can teach you how to properly cut the channel yourself, or as they say, teach you to channel the water.
5. These trained professionals will rather strongly ask you to join their group. They'll stress the importance of channeling properly or you might die. They'll also say that there's more you can do with that water than just power a mill, and they'll teach you that as well. And, once you qualify, you can join one of their subgroups, which each have their own specialty.

Level 2#

1. You are the mill. You will be receiving that water and learning how to let it flow through you to do different things with it.
2. It's not really water, it's the One Power.
3. That source of that not-water, the One Power, is known as the True Source.
4. We're going to keep that idea of "channeling"
5. There are threads to the One Power, and each person who can channel the One Power can usually grasp some threads better than others. These threads are named according to the sort of things that can be done using them - Earth, Air, Fire, Water, and Spirit - and are called the Five Powers
6. Not everyone can channel the One Power. Either you're born with it or you're not. You won't know if you can until you're a teenager or older.
7. Not everyone is able to channel the same amount of One Power. Some can channel only a little and some can channel a great deal. If you try to channel more than you're capable of, there's a good chance you'll burn out and never be able to channel again.
8. Both men and women can channel the One Power, but the men have a handicap which is explained in the books/series. They have named the power that men draw as saidin (pronounced sah-ih-DIN) and the power that women draw as saidar (pronounced sah-ih-DAHR).
9. Each task that you want to do with the One Power will need to be done with a mixture of threads of some or all of the Five Powers.
10. Putting those threads together in the right amount is known as Weaving.
11. There's a known set of Weaves that can be taught, such as Delving and Healing.
12. That group of professionals is known as the Aes Sedai (pronounced EYEZ seh-DEYE) and those specialty groups are known as Ajahs (pronounced AH-jah).
13. There are seven official Ajahs, each designated by a color: Blue, Red, White, Green, Brown, Yellow, Gray.

Here ends your lesson. :)