This is the dictionary meaning -
The prefix ‘pra’ means: forward, in front, on, forth, motion, or prakṛṣṭa, excellence, and 'dakṣiṇa' means: to the right.
प्रदक्षिण pradakSiNa adj. circumambulation from left to right of a person or object as a kind of worship
प्रदक्षिण pradakSiNa adj. standing or placed on the right
प्रदक्षिण pradakSiNa adj. turning the right side towards
प्रदक्षिण pradakSiNa adj. to the right side
प्रदक्षिण pradakSiNa adj. respectful
प्रदक्षिण pradakSiNa adj. auspicious
प्रदक्षिन pradakSina n. circumambulation [ in clockwise direction ]
प्रदक्षिणम् pradakSiNam ind. so that the reverential side is turned towards a person or object
In the story of the lifting of mount Govardhana, in chapter 24 of the 10th canto of the Bhāgavata, the supreme pradakṣiṇa, or Girirāja parikramā, was introduced -
10.24.29 pradakṣiṇaṁ ca kuruta go-viprānala-parvatān
Kṛṣṇa said - "Keep the cows, brahmins, fire and the mountain [Girirāja Govardhana] on your right as you go round them."
10.24.33 go-dhanāni puraskṛtya giriṁ cakruḥ pradakṣiṇam
“The Vrajavāsīs kept Girirāja Govardhana to their right during their parikramā."
As also after the completion of the Uddhava Gīta at the end of the 11th Canto:
11.29.45 sa evam ukto hari-medhasoddhavaḥ pradakṣiṇaṁ taṁ parisṛtya pādayoḥ
“Uddhava went round the Lord, keeping Him always to his right.”
In Vedic culture the superior is on the right and the subordinate on the left.
śrīdāma subalau vāme puro'sya madhumangalaḥ
dakṣiṇe śrī balascānye paritaḥ samupāviśan
(Govinda Līlāmṛta 4.22)
"(During Kṛṣṇa's breakfast) Śrīdāma and Subala sat on Kṛṣṇa's left, Madhumangala faced Him and Balarāma sat on His right........”
Balarāma, Kṛṣṇa's superior, sits on the right, and Śrīdāma and Subala, His subordinates, on the left.
dakṣiṇe'syāgrajau vāme'nujau putrau puraḥ sthitau;
subhadrādyā harer vāme baṭavo bala dakṣiṇe
(Govinda Līlāmṛta 20.44)
(During supper) "Nanda's older brothers (Upananda and Abhinanda) sat on his right, his younger brothers (Sananda and Nandana) on his left and Kṛṣṇa and Balarāma faced him. Subhadra and others sat on Kṛṣṇa's left and the brāhmaṇas sat on Balarāma's right."
I first learned the principle of junior to the left and senior to the right during my initiation from Sādhu Bābā in Vṛndāvana in 1982. I was asked to sit to Sādhu Bābā's left during the private ceremony.
The most famous verse mentioning pradakṣiṇa is: yāni kāni ca pāpāni brahma hatyādikāni ca tāni tāni pranaśyanti pradakṣiṇa pade pade (Which I cannot find in Haribhakti Vilāsa)
There is also a pradakṣiṇa māhātmya (glorification of pradakṣiṇa) in the 8th vilāsa of the Haribhakti Vilāsa.