A very witty phrase, if you ask me. Going by the definition by Wikipedia; “an idea is a concept or abstraction formed and existing in the mind. Human capability to contemplate ideas is associated with the ability of reasoning, self-reflection, and the ability to acquire and apply intellect. Further, ideas give rise to actual concepts, or mind generalizations, which are the basis for any kind of knowledge whether science or philosophy.”
So why do we say they rule the world? “Everything you see and touch was once an invisible idea until someone chose to bring into being.”- Richard Bach. Like a dream, an idea sprouts up in the mind, flies around in our brains till its used or naturally fades out. The uniqueness and power that set apart any successful businesses or individual, starts with the kind of ideas they come up with(usually influenced by their state of mind, environ and situations).