Wu Wei is an aspect of Taoism. Wu in English means no/negation and Wei means action. Wu Wei thus translated in English means no action or actionless-action. A more accurate translation is that by Alan Watts Non-forcing.
Some incorrectly believe Wu Wei is a call to inaction or cultivated passivity. Being lazy or avoiding the work that is supposed to be done. That isn't true. Tao Te Ching describes it this way: "The Way never acts, yet nothing is left undone." Wu Wei thus means spontaneous action. Action where you don't have to force things.
Wu Wei is said to be the principle that nature works on. Just like the growing of a plant. It takes no force and happens naturally of itself. Wu Wei implies we should act with the currents of life rather than against them.
Most athletes refer to it when they talk about the zone. A state where they don't think before acting and yet everything happens of itself. It's like a state of flow when the person is one with what he's doing.
Another example is that of a tree and a plant during a great storm. The small plant flows and bends with the wind and thus stays intact with its roots. The tree, however, stays rigid and eventually falls due to the extreme force of the wind.
The one practicing the art of Wu Wei is unaffected by adverse circumstances that might completely break the spirit and resolve of those that have a rigid philosophy or a controlling mindset.
Ultimately one who aligns with the Tao comes to see the world and surroundings not as separate entities but instead as interdependent objects in harmonious relationships with each other.