"A Gentle Breeze From The West" is not a specific term or title with a widely recognized meaning. It's possible it's a:

* Title of a song, book, painting, or other work of art: If you provide more context, I might be able to find it.

* Descriptive phrase used in literature or poetry: It could be a way to evoke a sense of peace or tranquility.

* A personal or informal name given to something: Perhaps it's the name of a horse, a dog, or a place.

Can you provide more information about where you encountered this phrase? That would help me understand what it refers to.