It becomes crowded during the krishnapaksha of Ashadha, after the Snana Yatra when devotees are not allowed to see the central icon of Jagannath (a form of Vishnu) in his Puri temple.
[1] Chaitanya Mahaprabhu during his stay in Puri used to see the deity form of Jagannath daily.
During Anavasara when Jagannath and his sibling deities were taken to the secret chamber for 15 days, he was unable to see the Lord.
So as per legend, Jagannath directed him to go to Brahmagiri and visit the Alarnath temple.
During Anavasara time the Kheeri bhoga offered to Alvarnaath Swami is much hyped and in demand.