External and Internal Forces:
Any given force can be either an external force or an internal force depending upon how the system is defined.
A system can be either a single object, or a group of objects. The objects do not even have to be bound or interacting with each other to form a system. However, it usually makes things a lot simpler if they are connected in some way.
Many times the constraints between the sub-bodies that comprise the system can be expressed as a mathematical relationship which will be useful when solving the problem.
Example: Simple Pendulum
A bob is connected to the end of a massless cord that is connected to the ceiling.
If one chooses the bob to be the system, then both the weight of the bob, mg, and the tension in the cord, Tc , are external forces.
If one chooses the cord to be the system, then there are two external forces acting on the cord: the force that the ceiling exerts on the cord and the force that the bob exerts on the cord. Both of these forces are equal in magnitude and equal to the tension in the cord by Newton's Third Law. If the cord were not massless, then there would be a third external force acting on this system, the weight of the cord. It would also mean that the two forces acting at its end would no longer be equal.
If one chooses both the bob and the cord to be a system, then there are two external forces acting on this system, the force of gravity on the bob and the force that the ceiling exerts on the cord. The forces that the cord exerts on the bob and the force that the bob exerts on the cord become internal force in this system. Moreover, by Newton's Third Law they are equal in magnitude and opposite in direction so that even if you considered them to be external forces, they would cancel each other out.
If you considered the bob, the cord, the ceiling, and the Earth to the system, then the only external forces acting on the system would be the gravitational force of the Moon and the Sun on this system. The weight of the bob would become an internal force balancing the force (also internal) that the bob exerts on the Earth. By Newton's Third Law the bob pulls on the Earth with a force equal to that which the Earth pulls on the bob, but in the opposite direction. It may be hard to believe, but it's true. You never notice it because the Earth's mass is so much bigger than the mass of ordinary objects.