Shaanti, meaning "peace", is a natural state of being. Disturbances are created either by us or others. For example, peace already exists in a place until someone makes noise. Therefore, peace underlies all our agitations. When agitations end, peace is naturally experienced since it was already there. Where there is peace, there is happiness. Therefore, every one without exception desires peace in his/her life.
However, peace within or without seems very hard to attain because it is covered by our own agitations. A rare few manage to remain peaceful within even in the midst of external agitation and troubles. To invoke peace, we chant prayers. By chanting prayers, troubles end and peace is experienced internally, irrespective of the external disturbances. All such prayers end by chanting shaanti thrice.
It is believed that trivaram satyam - that which is said thrice comes true. For emphasising a point we repeat a thing thrice. In the court of law also, one who takes the witness stands says, "I shall speak the truth, the whole truth and nothing but the truth".
The popular notion of peace today is 'absence of war'. But Hindus think of peace at three levels. We chant shaanti thrice to emphasize our intense desire for peace. All obstacles, problems and sorrows originate from three sources.
Aadhidaivika : The unseen divine forces over which we have little or no control like earthquakes, floods, volcanic eruptions etc.
Aadhibhautika: The known factors around us like accidents, human contacts, pollution, crime etc.
Aadhyaatmika: We sincerely pray to the Lord that at least while we undertake special tasks or even in our daily lives, there are no problems or that, problems are minimized from the three sources written about above.
May peace alone prevail. Hence shaanti is chanted thrice.
From www.balagokulam.org