This means phrase means a big deal or someone with fame and wealth. The big cheese can be the most influential or important person in a group, but it has often been used in a derogatory manner to refer to somebody self-important or vapid.
It came from England in the 19th century. The entomology is not 100% known, but some believe it has nothing to do with dairy products at all. There is the possibility that the saying came from someone mishearing the Hindi word chiz, meaning “a thing.” British colonialists might have picked up the term in India and adopted what they believe they had heard.
There’s no shortage of expressions involving cheese. For instance, one may be cheesed off (upset, annoyed, fed up), or someone may be cheesy (inauthentic, corny). But this particular expression specifically became a commonality with the British who would refer to someone as “quite the cheese” or “simply the cheese”