"go west" means to travel to seek your fortune, this phrase comes from American history, where some people would travel to the west of that continent where new riches like oil and gold were being discovered.

Aside from ''go west,'' there's another expression that conveys a similar meaning - ''to look for greener pasture.''

go west simply means to seek fortune

But my dictionary hasn't such a meaning "to travel to seek one's fortune". It gives the following meaning of this phrase 1) to die, to perish, 2) to go to America, 3) (the sun) beats down. That's why I want to join samurai samurai's question.