The following are some excerpts from that lecture.
Performing parikarama of the sacred Govardhan hill is most auspicious because it is an offering of worship to Radha and Krishna.
In the Srimad Bhagavatam it is mentioned how Lord Krishna ordered to the Vrajvasis that they worship Govardhan Hill. And a very important part of that worship was that all the gopas and the gopis circumambulated the Govardhan Hill, and in this way they could greatly, greatly please Lord Sri Krishna.
The real path of perfection is to follow in the footsteps of the great souls. Sri Chaitanya Mahaprabhu, when he came to Vrindavan, performed this Govardhan Parikrama. He saw every single stone of Govardhan Hill as non-different from the very body of Lord Sri Krishna. Even Madhavendra Puri performed the Govardhan Parikrama. Ishwar Puri, Nityananda Prabhu and Adwaita Prabhu, they all with great devotion circumambulated Sri Govardhan. The six Goswamis considered this Govardhan Parikrama as an integral part of their bhajan. Raghunath Das Goswami resided near Radha Kund at Govardhan Hill. Sanatana Goswami, while he was living here at Manasi Ganga at Chakleshwar Mahadev temple, he would do the Govardhan Parikrama every single day, even in his very old age. Similarly, other great Vaishnavas like Narottam Das Thakur and Srivas Acharya performed the Govardhan Parikrama. And then Vishwanath Chakravarty Thakur resided near Govardhan Hill. Srila Bhakti Siddahanta Sarasvati, Bhaktivinode, they had homes near Govardhan Hill and they would regularly do the Govardhan Parikrama. The Founder Acharya of ISKCON, A.C. Bhaktivedanta Swami Prabhupada, his last desire was that he wanted the devotees to take him on a Parikrama of Govardhan. In this way he established the most important and sacred nature of this worship.
The dust at the foot of Govardhan Hill that we walk upon, it is not only the sanctified dust of Braja, but it is also decorated with the dust of the lotus feet of all of these great incarnations and acharyas. It is said that in Vrindavan there are three items that are especially powerful to purify the heart: the dust of Braja, the river Yamuna and the Govardhan Hill.
The parikrama according to the advice of Srila Rupa Goswami should start by taking a bath in the beautiful Manasi Ganga Lake. One should commence the worship of Sri Giriraj by offering one’s body, mind and words during this Govardhan Parikrama.
– Radhanath Swami