Buddhism teaches us that the principal cause of suffering is craving, the desire for existence and personal gratification, the desire for a world of sights, sounds, smells, tastes, touch sensations, and ideas. The Third Noble Truth shows us that the key to overcoming this human predicament lies in eliminating craving. It was defined by the Buddha after his enlightenment as follows:
Now this, monks, is the noble truth of the cessation of suffering: it is the remainderless fading away and cessation of that same craving, the giving up and relinquishing of it, freedom from it, nonattachment. ~ In the Buddha’s Words
Here’s a wonderful talk given by Ven. Bhikkhu Bodhi on the meaning of the Third Noble Truth of Buddhism:

The Third Noble Truth, or Nibbana, has two dimensions: a psychological dimension and a philosophical dimension.
Psychological Dimension of Nibbana
First, the psychological dimension. We find that unhappiness, discontent or suffering results from the tension between desire and the lack of the thing desired. There are two possible approaches to overcoming the unhappiness that results from this tension. One is to obtain the object desired, to secure possession of it; the other is to eliminate the desire.
The Buddha’s teaching reverses the common assumption that happiness can be found by satisfying our desires. The things we want are inevitably impermanent and are bound to be lost either by chance or the passing of time. So even in the midst of happiness we become vulnerable to suffering. Therefore, the Buddha points out that true happiness is to be achieved by taking the opposite approach, the approach of eliminating our desires.
If we eliminate the desire our mind remains satisfied, content and happy no matter what our external situation may be. The Buddha says that this principle can be carried through all the way to the total uprooting of craving. This is the cessation of craving, the end of dukkha visible here and now.
Philosophical Dimension of Nibbana
But the end of dukkha has a more wide-ranging meaning than this. Craving drives us on over and over in samsara, the round of birth and death. When craving is eliminated, our actions no longer build up kamma, then the wheel of becoming is brought to a halt. This is the state of final deliverance which is the aim of the Buddha’s teaching.
The state of final deliverance is called Nibbana in Pali and Nirvana in Sanskrit. Nibbana literally means the extinguishing of a flame. The word Nibbana used by the Buddha means the extinguishing of the flame of craving, the extinguishing of the fires of greed, hatred, and delusion.
Nibbana is the ultimate goal of the Buddha’s path. The Buddha says, “Just as the water of a river plunges into the ocean and merges with the ocean, so the spiritual path, the Noble Eightfold Path, plunges into Nibbana and merges with Nibbana”
Complement with Ven. Bhikkhu Bodhi’s lecture on the First Noble Truth and the Second Noble Truth.
[…] Complement with Ven. Bhikkhu Bodhi’s lectures on the First Noble Truth, the Second Noble Truth, and the Third Noble Truth. […]