The Northern region of Bhāratavarṣa (Bharatavarsha;India) is called Āryāvarta (Aryavarta). It is said in Manusaṁhitā that the part of the land from the Himālaya(Himalaya) in the north to the Vindhya mountain in the south and between the two seas in the east and west ( the Bay of Bengal and the Arabian Sea) is Āryāvarta. —
āsamudrāttu vai pūrvādāsamudrāttu paścimāt
tayorevāntaraṁ giryorāryāvartṁ vidurbudhāḥ
This opinion is supported in Amarakoṣa.
Āryāvarta is presented as a part of Bhāratavarṣa (India) in Mahābhārata(Mahabharata).
Śukadeva (Sukadeva), the son of sage Vyāsa, in quest of salvation came to Āryāvarta by crossing many countries.It is said in a śloka (sloka; verse) of Śāntiparva that by passing over China and the land of the Hūnas Śukadeva entered into Āryāvarta —
sa deān vividhān paśyaṃcīnahūnaniveśitān
āryāvatamimaṃ deśamājagāma mahāmuniḥ.
From this it is clearly understandable that through modern China and Middle Asia Śukadeva entered into Āryāvarta. So it may be conceived that the very North India at the foot of the Himālaya was the ancient Āryāvarta.
The name of Ikṣvāku(Ikshvaku) dynasty is inseparably mixed up/ diffused/pervading with Āryāvarta. Among the one hundred sons of Ikṣvāku, twenty five reigned the eastern part of Āryāvarta, other twenty five ruled over the western part, three the middle part, and the rest to the south and north portion.
After killing of the Kṣatriyas(Kshatriya) Paraśurāma(Parasurama) performed a vast and pompous Vedic sacrifice. after the completion of salvation he gifted the Preceptor (Upadraṣā) some land in Āryāvarta.
It is already mentioned that according to Manu, the part between the rivers Sarasvatī (Saraswati) and Dṛṣadvatī(Drishavati) ,that is, if the modern Panjab is taken undivided,then the middle part of it was known as Āryāvarta. The modern scholars opines that the river Dṛṣadvatī streamed near the region of river Sarasvatī. If we consider the views of Manu as well as that of the modern scholars, it is comprehended that Āryāvarta was merely a small part of land between these two rivers. This part of land is regarded as auspicious one in the Ṛṛgveda(Rigveda) too. [Ṛgveda 3.23.4]
It is marked as a worthy place for special worship in 25th Brāhmaṇa (Brahmana; part of the Vedic Scripture) and Kātyāyana Śrautasūtra (Katyayana Srautasutra). [ Pañcaviṃśa Brāhmaṇa (Caland) 25.1011-16; Kātyāyana Śroutasūtra 24.6.3]
Brahmarṣideśa (Brahmarshidesa) was situated at the south and south-east border of Āryāvarta.
The Brahmarṣideśa was situated at the south and south-east border of Āryāvarta. ‘Brahmarṣideśa’ referred to the region that included Kurukṣetra, Śuasena, Pāñcāla and Matsya. The Aryans lived towards the east of this Brahmarṣidesa. In the opinion of many, the region between the rivers Gaṇgā and Yamunā is Āryāvarta.
Others have provided a more detailed definition of Āryāvarta. According to them, the western part of Āryāvarta was known as Brahmāvarta.