Pooh-Bah is a character in Gilbert and Sullivan's comic opera The Mikado (1885). When a cheap tailor named Ko-Ko was given a rank as Lord-High-Executioner, many officials refused to serve under someone who had been a peasant. Pooh-Bah was so haughty that he did not mind continuing to serve, so he accepted all of their positions as well as all of their salaries. Whenever Pooh-Bah shows up anywhere, it means most of the towns officials have shown up, as he carries the titles. Hence, Pooh-Bah was designated Lord-High-Everything-Else, because his titles were too numerous to mention every time someone addressed him.
It is still common in modern performances of the play that when at some points his titles are enumerated, in addition to those scripted, people will add many more modern references to jobs that he might hold as a source of humor.
When you now call someone a Pooh-Bah (sometimes spelled Poohbah), you are saying they are either a very self-important person, or someone who holds many offices at the same time.