Photo: 1944 Signatories, Chicago Convention (Public Domain).
Cabotage is simply the legal way of saying transporting people and things within a country. If that country is not your own, you may need permission to do that. The penalty for making a mistake here can be severe, so you need to be smart about the subject if you plan on making multiple stops in a country with people and things you didn't bring with you in the first place.
What follows comes from the references shown below. Where I think it helpful, I've added my own comments in blue.
Cabotage: air transport of passengers and goods within the same national territory.
[AC 91-70A Oceanic Operations, ¶3-1.n.] Private pilots and commercial operators should understand cabotage, formally defined as “Air transport of passengers and goods within the same national territory.” The definition adopted by ICAO at the Chicago Convention is as follows: “Each state shall have the right to refuse permission to the aircraft of other contracting states to take on its territory passengers, mail, and cargo destined for another point within its territory.” Although cabotage rules are different in various countries and usually incorporate the term “for hire,” some countries do not allow foreign aircraft within their boundaries to carry even non-revenue passengers. The restrictions range from no restrictions to not allowed. The fines for cabotage can be extremely high; therefore, pilots and flight departments should be absolutely sure of a country’s cabotage rules before carrying passengers. The corporate aircraft restraints section for each country in the IFIM list the cabotage requirements and restrictions of individual countries. Refer to chapter II, article 7 of the Chicago Convention.
Generally speaking, you cannot fly to some foreign countries, pick up local citizens and transport them within that country. Not all countries have cabotage restrictions and many that do will allow exceptions if the citizens are employees of a company associated with the airplane. The rules vary by country and you need to ensure you follow them. AC 91-70A, ¶3- 1.n. offers an FAA web page that was very helpful in determining country-specific cabotage rules but that service is no longer offered. You are left to ask your flight planning service provider or looking for the country’s AIP.
So what is this convention we hear so much about? During World War II it became obvious that having a bunch of airplanes from different countries share the same airspace wouldn't work if they all used the operating rules and standards from their home countries. The powers that be met in Chicago and agreed upon a set of rules that became known as the Convention on International Civil Aviation Done at Chicago on the 7th Day of December 1944.
[ICAO Chicago Convention Article 7]. Each contracting state shall have the right to refuse permission to the aircraft or other contracting States to take on in its territory passengers, mail and cargo carried for remuneration or hire and destined for another point within its territory. Each contracting State undertakes not to enter into any arrangements which specifically grant any such privilege on an exclusive basis to any other State or airline of any other State, and not to obtain any such exclusive privilege from any other State.
While the web site recommended by AC 91-70A is quite good and worth viewing prior to every trip, it doesn't offer much help with cabotage. The next step is to the particular country's International Flight Information Manual (IFIM), but those aren't easy to come by. I've found the best course of action is to use an international handler, like Air Routing or Universal, with boots on the ground in country. Tell them what you plan to do and ask "is it legal? and "will the local authorities object?"
You might be tempted to blow the entire topic off, thinking you are not operating for remuneration or hire. Think again, many countries have expanded the definition to include just about any business purpose.
Thankfully, many countries consider an employee of a multinational a part of a U.S. branch of the same company. I've done this as a pilot for Compaq Computer, for example: flown German nationals employed by Compaq in Germany within points in Germany. We asked the local authorities first who did not object. Ask first!
Portions of this page can be found in the book International Flight Operations, Part VIII, Chapter 10.
Advisory Circular 91-70A, Oceanic and International Operations, 8/12/10, U.S. Department of Transportation