Atirātra (Atiratra) is a special kind of a yajña (yajna) or yāga (yaga), a type of Somayāga (Somayaga). Its ancientness can be guessed from its mention in Ṛgveda (Rigveda) –

brāhmaṇāso atirātre na some/ saro na pūrṇamabhito vadantaḥ

During night, in three segments of paryāya (paryaya) Atirātra is observed. In each segment a cup full of somarasa (the revered, divine beverage of ancient India) is sent around the four priests or ṛttvika (rittwika). During each circulation of the goblet, one śastra (sastra) and one yājyā (yajya), types of verses from Sāmaveda (Samaveda), are recited and after chanting the latter, oblation of somarasa is made to the fire. Each of the three segments sees circulation of the cups of the priests called hotā (hota), maitrāvaruṇa (maitravaruna), brāhmaṇācchaṃsī (brahmanachchhamsi) and acchāvāk (achchhavak) in respective order. Because the cups are circulated or sent around, each segment is called a paryāya. According to Āpastamba Śrautasūtra (Apstamba Srautasutra), preparations of Atirātra yajña starts in the daytime and continues till late in the night. Throughout the day and the night twenty-nine śastra and twenty-nine verses are chanted. 

A night constituting of thirty daṇḍa (danda; a measure of time) can be divided in three segments each comprising ten daṇḍa. These three segments become three paryāya of Atirātra yajña. Since its ending late at night till dawn, hotā chants more than a thousand Rigvedic verses which are collectively called Aśvin-śastra (Aswin-sastra). To say so, Atirātra yajña is a deformed version of Agniṣṭoma yajña which sees a minor ritual in the daytime and three extra oblations of somarasa in three segments of night. 

[Vaidik Yuger Yagyagya, Santi Bandyopadhyay, Pp. 50, 74]

Aitareya Brāhmaṇa (Aitareya Brahmana) narrates a story about the inception of Atirātra yāga. Once the combatting parties of the gods and the demons took shelter in day and night respectively; and as both parties equalled each other in strength, none could be defeated by the other. Given this situation, Indra called, “Is there anybody to help me oust these demons from the shelter of darkness of night?” Nobody replied to Indra’s call, for everyone was scared of the darkness of night (this indicates at the root of the mortal world’s fear at the darkness of night, which is regarded as the second self of death).

But the Vedic rhymes (chanda; chhanda), like Gāyatrī (Gayatri), Jagatī (Jagati), Triṣṭubha (Trishtubha), Anuṣṭupa (Anushtupa) and so on, followed Indra in his adventure. Hence, the nocturnal rituals of Atirātra is performed only with help of the Vedic rhymes and Indra as their deity. It is said that through these rituals (performed in the three segments) Indra encompassed the entire kingdom (symbolised by the space of yajña) and uprooted the demons from the shelter of night’s darkness. The rhymes, it is said, told Indra, “My Lord! We have followed you to remove the demons from the darkness of śarbarī (sarbari; night).” Since then these rhymes are known as atiśarbara (atisarbara), or the one(s) who win(s) over night. It was by means of these rhymes that Indra had been able to conquer night and darkness, and therein lies the significance of this name of the rhymes. In fact, in these rituals the hymns hail Indra himself as Atiśarbara –

indrāya tvā atiśarbarāya.

According to Kālikāpurāṇa (Kalikapurana), from beneath the tongue of the sacrificial boar (yajñabarāha; yajnabaraha) two yajña, namely Atirātra and Vairāja (Vairaja), originated.