The person in charge. Eliminates the need to know the title of the person in charge. Is sometimes used derogatorily especially when refering to a person of low rank or authority. A jibby can be a supervisor, foreman, superintendent, captain, manager, boss, landlord, team leader etc.
If you were to walk into a store and say to someone who worked there, "where is the jibby?" you would not need to know the title of the person in charge, such as store manager, supervisor etc.
The jibby told me I had to work today.
Ask the jibby if we can sit here.