The cloud it fixed relative to the air mass.
The air mass moves relative to you (that is what you feel as "wind").
When an air mass moves, it is usually because of a "pressure gradient": the air tries to go from a place of high pressure (H) to a place of low pressure (L).
So far so good.
The reason we have Highs and Lows is often because of unequal heating of Earth, and that is partly because of the rotation (one side is day, the other side is night and the whole thing keeps changing).
The role of the rotation is a bit complicated, but it comes after all the above. Because the Earth rotates, the heating zone keeps going westward. Heating causes Lows (hot air is lighter).
Air is coolest just before sunrise (therefore, pressure is maximum) and the air gets warmer as the day progresses (the air is warmer as you move east of the sunrise line).. Therefore, the general movement is for air to go from west to east (e.g., jet stream).
Then, as the air tries to hit the Low pressure centre, the Low moves (because of Earth's rotation, so that the air keeps missing, and ends up in a spiral around the Low (counterclockwise in the northern hemisphere).
So, locally, if you are close to a Low pressure which passes between you and the equator, then the local wind will come from the west.
In general, clouds simply follow the air masses. Because the air moves relative to you, then the clouds simply go along for the ride.