The word man means to think – and a mantra is a thought or a sensation expressed through sound. It can consist of one or more sounds that has no actual meaning. Or it can consist of meaningful sentences.
The most well-known and the oldest of all mantras is OM, which symbolizes the universal power and is said to be the source of all sounds. OM and other mantras are used for meditation where they are thought to take the individual to a higher level of consciousness when repeated over and over again (called japa). The vibration of the sound of the mantra merges into the vibration of thought and generates mental serenity.
In yoga we (often) begin and end the practice with a non-religious mantra. It is a nice and respectful way to round off the practice.The opening mantra helps to focus the attention on the breath before starting the yoga practice.
Mantra is generally learned first though repetition, and, once familiar, meaning is found and the mantra analyzed.
Opening Mantra of the Ashtanga Yoga practice
Vande gurunam caranaravinde
Sandarsita svatma sukhavabodhe
Samsara halahala mohasantyai
Sahasra sirasam svetam
I honor the lotus feet of all the teachers
which awaken and manifest joy in one’s true self
beyond comparison, acting as the jungle physician;
for pacifying the poisonous delusion of the cycle of birth and deathIn the form of a man up to the shoulders;
holding a conch shell ( divine sound), a discus ( wheel of time),
and a sword (discrimination), one thousand-headed and white;
I bow respectfully to Patanjali
Closing Mantra of the Ashtanga Yoga practice
Swashti Praja Bhyah Pari Pala Yantam
Nya Yena Margena Mahi Mahishaha
Lokaa Samastha Sukhino Bhavanhtu
Om Shanti Shanti Shanti
May all be well with mankind
May the leaders of the earth protect in every way by keeping to the right path
May there there be goodness for those who know the earth to be sacred
And may people of the world be happy and prosperous
Om peace peace peace
The essence of the closing mantra is to wish for peace, prosperity and happiness for all creations of the world.