What are the primary causes for the wind on Earth?

Short answer; temperature.

Air is largely affected by temperature, which causes hotter air to rise above colder air. The sun is always heating a portion of the Earth, but not others, creating a hot spot which change the air temperature.

Next major item is humidity or moisture content. the more water vapor present the heavier the air (which pushes it downward), but it can be heated more with less sunlight or other form of energy.

Next, we have height. Air near land has higher pressure than air at high altitudes. Which means air near the surface of the planet can more easily retain heat and air at high altitudes shed heat more quickly. This also causes dynamic of flows of differing densities, but that is likely outside the topic.

Lastly, we have obstacles such as mountains, trees, and buildings. As air passes around objects it changes the speed and denisty of the air, subject to the shape of the object.

After all of this you get gusts of wind, wind storms, or no wind at all. The mapping of, and predicting of wind is amongst the most sophisticated sciences we have today as it requires knowing as much of the conditions across the Earth and the things that may change those conditions. And you can see from the weather reports how often we get it right and how often we get it wrong.