Hi, I’m not actually that knowledgeable on the subject, but to my understanding, it refers to an unstable form of government that is basically being controlled by foreign companies. The Wikipedia page explains where the term comes from and what it means:
Also, if it is of interest to you, here is the page for kleptocracy, which is basically the technical term for what a banana republic is.
Incidentally, Banana Republic is also the name of a clothing retailer in the US.