The wheel of life, or "samsara", is an ancient symbol that has the same meaning in Buddhism and Hinduism. It is symbolizes the cycle of birth, life, and death. When one revolution of the wheel is completed, life begins again with rebirth.
What is karma?
Karma is a Sanskrit word that literally means "action". The word is used to refer to volitional acts as well as the forces that arise from these acts. The idea of karma had existed in ancient Indian philosophy before the time of Siddhartha Gautama, and it became an important element of Buddhist philosophy.
The Hindu and Buddhist concepts of karma are quite similar, although Hinduism makes a further distinction between different types of karma, such as present karma, latent karma, and future karma. In the understanding of both thought systems, the law of karma describes the connection between actions and the resulting forces, as follows: wholesome actions lead to wholesome states while unwholesome actions lead to a unwholesome states, individually as well as collectively.
The ethical dimension.
To make this more intelligible, one has to account for (un)wholesome actions and (un)wholesome states and their respective meaning in Buddhism. The former is outlined in the Noble Eightfold Path. Action springs from volition, which springs from intention, which springs from thought, and so forth. The quality of actions can be described in ethical terms, simply as either good or bad, or both good and bad, or indifferent.
There are various grades of ethical qualities; and most people have an intuitive understanding that enables them to discern between good and bad, although the discerning ability depends on the person's state of mental development. A wise person at a high level of mental development can clearly discern mental activities and actions in an ethical dimension, while a deluded person has difficulties or is even unable to do so.
Good and bad vs. skillful and unskillful.
Wherever the three defilements - delusion, greed, and aversion - are present, they blur the view and increase the level of confusion in the individual or group. Consequently, if the defilements are present, there is a low level of skill in distinguishing between good and bad actions. Thus it makes sense to say that we have skillful (good) and unskillful (bad) thoughts, we speak skillful (good) and unskillful (bad) words, and we act either in a skillful (good) or in an unskillful (bad) way.
The Buddhist Precepts and the Ten Perfections give concrete meaning to good and bad and explain skillful and unskillful volitional acts in detail. Since everything in Buddhism is interrelated, the Eightfold Path must be seen in connection with the Four Noble Truths, the concept of karma, and the tenet of rebirth.
Moral quality of volitional acts determines karma.
The law of karma states that there is a connection between the moral quality, the level of skill in volitional actions, and the resulting states. What we are is determined largely by what we thought, said and did in the past, while what we are thinking, saying, and doing now will form our future. The karma of past, present, and future events are connected by the law of cause and effect.
For instance, if one generates bad karma by hurting or killing sentient beings, one will have to endure the negative consequences of these deeds in this or another lifetime. Similarly, if one generates good karma by observing the precepts, positive consequences will follow inevitably.
Buddhists understand karma as a natural law. There is no higher instance, no judgment, no divine intervention, and no gods that steer man's destiny, but only the law of karma itself, which works on a global time frame. Deeds yield consequences either in the next second, in the next hour, day, month, year, decade, or even in the next lifetime, or in another distant lifetime. To illustrate this, consider the following example describing a sequence of volitional acts, which yield instant karmic results:
Example: The arising of volition and karma.
An unpleasant sensation occurs. A thought arises that the source of the unpleasantness was a person. This thought is a delusion; any decisions based upon it will therefore be unskillful. A thought arises that some past sensations of unpleasantness issued from this same person. This thought is a further delusion. This is followed by a willful decision to speak words that will produce an unpleasant sensation in that which is perceived as a person. This decision is an act of hostility.
Of all the events described so far, only this is called karma. Words are carefully chosen in the hopes that when heard they will cause pain. The words are pronounced aloud. This is the execution of the decision to be hostile. It may also be classed as a kind of karma, although technically it is after-karma.
There is a visual sensation of a furrowed brow and turned down mouth. The thought arises that the other person's face is frowning. The thought arises that the other person's feelings were hurt. There is a fleeting joyful feeling of success in knowing that one has scored a damaging verbal blow.
Eventually, perhaps much later, there is an unpleasant sensation of regret, perhaps taking the form of a sensation of fear that the perceived enemy may retaliate, or perhaps taking the form of remorse on having acted impetuously, like an immature child, and hoping that no one will remember this childish action. This regret or fear is the unpleasant ripening of the karma, the unskillful decision to inflict pain through words.
Rebirth.
Buddhists hold that the retributive process of karma can span more than one lifetime. Rebirth, or reincarnation, has always been an important tenet in Buddhism; and it is often referred to as walking the wheel of life (samsara). It is the process of being born over and over again in different times and different situations, possibly for many thousand times.
As long as there is delusion, greed, and aversion, and as long as passions are not extinguished, we generate karma. Because we eventually accumulate unmaterialized karma in this or in a past lifetime, there is a next lifetime in which the accumulated karma will take form. Only when all accumulated karma is realized and the generation of new karma is calmed, one can enter the stream that leads to Nirvana. This process continues until Nirvana is reached, which signifies the cessation of rebirth and, hence, suffering.
It is notable that this also entails the avoidance of "good karma". Once the stream that leads to Nirvana is entered, creating wholesome karma is not an object anymore. Although wholesome karma leads to entering the stream, it does not necessarily lead to Nirvana, only the extinguishment of all karmic forces will lead to Nirvana.
The Non-Self.
The concept of rebirth is unfamiliar to most Western people. Its philosophical and traditional foundation is found in India, where the theory of transmigration of souls had presumably existed long before it was written down in the Upanishads around 300 BC.
The Buddhist concept is subtly different from the classical Indian understanding, because it denies the existence of a self. In Buddhism, the idea of self is merely an illusion. Man wrongly identifies perception, consciousness, mind and body with what he calls self. In reality there is no abiding entity that could be identified with a self, because the states of perception, consciousness, and mind constantly change.
The body is mortal and when it dies, consciousness and all mental activities cease. That is why there is no soul. The idea of soul is simply an extension of the self. Soul is the immortal version of the self that supposedly survives physical death. Since we know that consciousness is a function of our nervous system, it seems difficult to believe that the conscious self survives death. Hence, Buddhists deny the reality of both self and soul.
The idea of an abiding self is deceptive, because it is derived from unenlightened reasoning. The word self simply provides a reference frame for the mind-body phenomena of sentient beings. We usually identify it with our body and the stream of consciousness induced by sense perceptions and thoughts. In reality, what we call self is neither abiding nor detached from the rest of the world and other beings. Buddhists call this the "neither self nor non-self".
What is reborn if not the "self"?
If the idea of non-self sounds odd, then it must sound even more curious that non-self can be reborn. There is a seeming contradiction between the canon of rebirth and that of the non-self, which even many dedicated Buddhists find difficult to understand. The contradiction is, however, only on the surface and can be solved if one pictures the self as the result of karmic formation. This can be put into less abstract words:

If we imagine the world as an ocean, we are like the ripples on the ocean. Formations like ripples and waves occur, because of wind, tides, and other kinetic forces. In the Buddhist analogy, the universe is in motion due to karmic forces. A ripple, a wave, or a billow may seem as an individual entity for a moment, creating the illusion that it has a self, but it is gone in the next moment. The truth is that all individuals are one. A ripple is a temporary phenomenon; it is just water in motion. We know that kinetic energy causes wave forms on a body of water and it would be ridiculous to say that a single ripple or wave has a self.
Similarly, in case of beings, the process of coming into life and being conditioned in a particular way is caused by karmic forces. The up and down of the ocean's waves corresponds with the rotation of the wheel of life. The sea that surges, falls, and resurges, is the life that is born, dies, and is reborn again. It is therefore obvious that we should not focus on the temporary phenomenon of the wave, but on the force that causes, forms, and drives it. Nothing else is said, although in more practical terms, in the Eightfold Path.