The Axiom of Causality is the proposition that everything in the universe has a cause and is thus an effect of that cause. This means that if a given event occurs, then this is the result of a previous, related event. If an object is in a certain state, then it is in that state as a result of another object interacting with it previously. For example, if a baseball is moving through the air, it must be moving this way because of a previous interaction with another object, such as being hit by a baseball bat.
An epistemological axiom is a self-evident truth. Thus the "Axiom of Causality" implicitly claims to be a universal rule that is so obvious that it does not need to be proved to be accepted. Even among epistemologists, the existence of such a rule is controversial. See the full article on Epistemology.
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One implication of the Axiom is that if a phenomenon appears to occur without any observable external cause, there must be an internal force or mechanism causing the phenomenon. Quantum mechanics appears to violate the Axiom because elementary particles exhibit behavior without any observable external cause, and no internal mechanisms have yet been observed within them.
Another implication of the Axiom is that all variation in the universe is a result of the logical and continual application of the physical laws. Specifically, all effects in the universe are the logical result of the transfer of energy from one form to another, from one place to another, and the outcome is dictated by the rules of the universe.
The baseball flies through the air because the bat imparted kinetic energy to the ball. An object cannot accelerate without being imparted energy from another object, but if so then according to the laws of thermodynamics, it must be consuming its own stored energy through an internal mechanism. Magnets may appear to violate this because they seem to cause acceleration without depleting an energy reservoir. Magnets store energy in the form of a magnetic field, but this energy does not appear to deplete no matter how much energy it transfers to external objects. But magnets do follow the laws of thermodynamics, because the potential energy of the structure of objects within magnetic fields is irretrievably converted to kinetic energy during attraction. Furthermore, creating magnets (magnetizing ferro-magnetic materials) requires energy.
If all causes have effects, and all effects logically follow the rules of the universe, then all events follow a theoretically predictable pattern, thus all future events have already been determined by past events. See the full article on Determinism.
If all effects are the result of previous causes, forming a logical chain of events, then the cause of a given effect must itself be the effect of a previous cause, which itself is the effect of a previous cause, and so on. Therefore we could at least conceive of a situation where one could trace each cause to the one before it. One possibility is that this process would go on forever, with each event being the result of a previous event. This runs contrary the human intuition that everything has a beginning and an end. Another possibility is that the process would trace back finally to a first cause, or simultaneous group of first causes. See the full article on Cosmogony.