The One Power. Saidin and saidar, the male and female half of the One Power working in concert, turning the Wheel of Time. The One Power flows from the True Source. Wielding the One Power could be readily be described as pulling the fabric of reality and weaving it into a form to fit your will.
Wielders of saidin, Asha'man, must wrestle and struggle against the flow of saidin to weave the One Power.
Wielders of saidar, Aes Sedai, must surrender to the flow of saidar to weave their flows of the One Power.
To wield the One Power, the channeler must pull the the threads of power to shape the effect they desire. A certain way of executing an effect is called a "weave". The effect and form change depending on the types of power used in forming the weave.
The One Power is composed of five separate elements, which are Air, Earth, Fire, Water, and Spirit.
People unable to channel the One Power are unable to see the weaves, and only people of the same gender can see the weaves. Men can sense when women embrace the One Power but not vice versa.