The Kinetic Chain, not to be confused with the Kinematic Chain, is a term to describe a chain of events, and forces used to create them, in the Human Movement System. Many sports professionals use this term very frequently, yet very few actually understand what it really means and how the kinetic chain can be described through various movements performed by the body.
What is the Kinetic Chain
Movement is created by 3 different systems in the human body, known as the muscular system, skeletal system and nervous system. Through the joints of the skeletal system, the nerves and muscles must work in harmony, in a chain-linked fashion, to produce movement. This is the kinetic chain.
Remember the old song when you were a kid that said "the hip bone's connected to the thigh bone", etc? Well, this is how the kinetic chain works. Our joints are a huge part of the kinetic chain, although there's really not one part that's more important than the other, as there would be no human movement without any of the 3 systems we discussed above.
When any of the links within human movement(s) are broken, the movement itself will be affected. If you were to sprain your ankle you would notice that you are forced to move differently than before, which is how the chain is affected, but not necessarily broken, as Mike Reinold discusses here. Another point that he brings up (a very good one), is that the theory of 3 systems (as discussed above) is a bit too simplistic, as ligaments, tendons and fascia are not discussed.
Without tendons we are left with limited stability of the joint (chain), and without tendons (muscles are mentioned, but not referred to as musculotendinous) there's issues with the force being applied. Without fascia we are leaving out more issues with stability and mobility at certain 'chains'.
Open-chain and Closed-chain Movements
Another term(s) you may have run into is open or closed kinetic (OKC/CKC) movements.
Open-chain or Open Kinetic Chain (OKC) movements are movements in which the distal extremeties, whether it be hands or feet, are not in a closed (or 'fixed') position, such as standing or hands against an object, and can be moved freely. For instance, if you were doing a push-up you would be in a closed-chain movement, whereas an open-chain movement would be in a bench press position (feet can move freely). Something else to consider is the force being applied in these positions. In an OKC movement the force applied must be greater than the resistant forces, such as the ground forces or extremely heavy/immovable objects.
Closed-chain or Closed Kinetic Chain (CKC) movements in which the distal extremeties (hands or feet) are in a fixed position and there is not enough applied force to move the object. Movements such as these are push-ups, squats, deadlifts, pull-ups and lunges.
References: Lippincott Williams & Wilkins (2007). NASM Essentials of Personal Fitness Training (3rd edition)