Generally, they are recited at the beginning and end of religious rituals and discourses.
Shanti Mantras are invoked in the beginning of some topics of the Upanishads.
Prior understanding of Vedanta is essential for translation and explanation of these Mantra.
The Brihadaranyaka Upanishad explains Consciousness and it in this context that this Shanti Mantra needs to be understood.ॐ शं नो मित्रः शं वरुणः। शं नो भवत्वर्यमा। शं न इन्द्रो बृहस्पतिः। शं नो विष्णुरुरुक्रमः। नमो ब्रह्मणे। नमस्ते वायो। त्वमेव प्रत्यक्षं ब्रह्मासि। त्वामेव प्रत्यक्षम् ब्रह्म वदिष्यामि। ॠतं वदिष्यामि। सत्यं वदिष्यामि। तन्मामवतु। तद्वक्तारमवतु। अवतु माम्। अवतु वक्तारम्। ॐ शान्तिः शान्तिः शान्तिः॥ [3] Oṃ śaṃ no mitraḥ śaṃ varuṇaḥ | śaṃ no bhavatv aryamā | śaṃ na indro bṛhaspatiḥ | śaṃ no viṣṇur urukramaḥ | namo brahmaṇe | namaste vāyo | tvam eva pratyakṣaṃ bhrahmāsi | tvām eva pratyakṣam brahma vadiṣyāmi | ṝtaṃ vadiṣyāmi | satyaṃ vadiṣyāmi | tan mām avatu | tad vaktāram avatu | avatu mām | avatu vaktāram | Oṃ śāntiḥ śāntiḥ śāntiḥ || Om May Mitra be blissful to us.
Identifying oneself here as "the reciter", and not as "I", is a sign of self-realization, of transcending beyond self and ego being dissolved.
ॐ सह नाववतु | सह नौ भुनक्तु | सह वीर्यं करवावहै | तेजस्विनावधीतमस्तु मा विद्विषावहै॥ ॐ शान्तिः शान्तिः शान्तिः॥ Oṃ saha nāv avatu saha nau bhunaktu saha vīryaṃ karavāvahai tejasvi nāv adhītam astu mā vidviṣāvahai | Oṃ śāntiḥ śāntiḥ śāntiḥ ||
May God protect us both together; May God nourish us both together; May we work conjointly with great energy; May our study be vigorous and effective, and may we not mutually dispute (or may we not hate any); Om!
[5] ॐ आप्यायन्तु ममाङ्गानि वाक्प्राणश्चक्षुः श्रोत्रमथो बलमिन्द्रियाणि च सर्वाणि। सर्वम् ब्रह्मोपनिषदम् माऽहं ब्रह्म निराकुर्यां मा मा ब्रह्म निराकरोदनिराकरणमस्त्वनिराकरणम् मेऽस्तु। तदात्मनि निरते य उपनिषत्सु धर्मास्ते मयि सन्तु ते मयि सन्तु। ॐ शान्तिः शान्तिः शान्तिः॥ [6] oṃ āpyāyantu mamāṅgāni vākprāṇaścakṣuḥ śrotram atho balam indriyāṇi ca sarvāṇi | sarvam brahma upaniṣadam mā'haṃ brahma nirākuryāṃ mā mā brahma nirākarodanirākaraṇamastvanirākaraṇam me 'stu | tadātmani nirate ya upaniṣatsu dharmāste mayi santu te mayi santu | oṃ śāntiḥ śāntiḥ śāntiḥ || Om!
May my limbs, speech, vital air, eyes, ears, strength, And all the senses be fully developed.
May all the Dharmas extolled by the Upanishads shine in me Who am intent on knowing the Self.
I shall join together (i.e. obliterate the difference of) day And night through this study.
[9] ॐ भद्रं कर्णेभिः श्रृणुयाम देवाः। भद्रं पश्येमाक्षभिर्यजत्राः स्थिरैरङ्गैस्तुष्टुवाग्ंसस्तनूभिः। व्यशेम देवहितम् यदायुः। स्वस्ति न इन्द्रो वृद्धश्रवाः। स्वस्ति नः पूषा विश्ववेदाः। स्वस्ति नस्तार्क्ष्यो अरिष्टनेमिः। स्वस्ति नो बृहस्पतिर्दधातु॥ ॐ शान्तिः शान्तिः शान्तिः॥ [10][11] oṃ bhadraṃ karṇebhiḥ śṛṇuyāma devāḥ | bhadraṃ paśyemākṣabhir yajatrāḥ sthirair aṅgais tuṣṭuvāgṁsas tanūbhiḥ | vyaśema devahitam yadāyuḥ | svasti na indro vṛddhaśravāḥ | svasti naḥ pūṣā viśvavedāḥ | svasti nas tārkṣyo ariṣṭanemiḥ | svasti no bṛhaspatir dadhātu oṃ śāntiḥ śāntiḥ śāntiḥ || Om!
May peace reign all over this earth, in water and in all herbs, trees and creepers.
— (Translation by Swami Abhedananda, Ramakrishna Vedanta Math, India) ॐ असतो मा सद्गमय । तमसो मा ज्योतिर्गमय । मृत्योर्माऽमृतं गमय ॥ ॐ शान्तिः शान्तिः शान्तिः ॥ oṃ asato mā sad gamaya tamaso mā jyotir gamaya mṛtyor mā 'mṛtaṃ gamaya oṃ śāntiḥ śāntiḥ śāntiḥ Not towards the unreal, lead us to the real Not towards darkness, lead us to light Not towards death, lead us to immortality Om peace, peace, peace!
ॐ सर्वेषाऺ स्वस्तिर्भवतु । सर्वेषाऺ शान्तिर्भवतु । सर्वेषाऺ पूर्णं भवतु । सर्वेषाऺ मङ्गलं भवतु । ॐ शान्तिः शान्तिः शान्तिः ॥ oṃ sarveṣāṃ svastir bhavatu | sarveṣāṃ śāntir bhavatu | sarveṣāṃ pūrṇaṃ bhavatu | sarveṣāṃ maṅgalaṃ-bhavatu | oṃ śāntiḥ śāntiḥ śāntiḥ || 1: May there be Well-Being in All, 2: May there be Peace in All, 3: May there be Fulfilment in All, 4: May there be Auspiciousness in All, 5: Om Peace, Peace, Peace.
— (Translation by Swami Abhedananda, Ramakrishna Vedanta Math, India)