This forest is called Belvan because, during Krishna's manifest pastimes, there was an abundance of bel (bilva) trees here. While grazing the cows in this most captivating and pleasant forest, Shri Krishna and His sakhas would play different kinds of sports and relish the ripe bel fruits.
This is described in BhaktiRatnakar: Ram Krishna sakha saha e bilvavanete pakka bilvaphala bhunje mahakautukete "It was here that Rama and Krishna along with their sakhas ate ripe bilva fruits with great festivity."
Once,goddess Lakshmi heard a description from the mouth of Narad about Vrajendra-nandan Shri Krishna's sweet ras-lila and the good fortune of the gopis. An eagerness to behold this ras-lila arose in her heart. No one but the gopis has the qualification to enter ras-lila, since they are the true emblem of undivided and pure prem. It is only possible to gain entrance into ras-lila by receiving the mercy of Radhika, the embodiment of mahabhav and the crest jewel of all Krishna's beloveds, and by the mercy of Her true representatives, the gopis. At that time, one can gain entrance very easily. Thus, to enter the ras-lila Lakshmi began performing severe austerities at this place, but to no avail. To this day, she is performing austerities here with this desire. In Shrimad-Bhagavata, the wives of the serpent Kaliya] refer to this pastime in their prayers to Shri Krishna: "Bhagvan, we are unable to understand what sadhana Kaliyanag performed that He became a proprietor of the dust of Your lotus feet. It is so rare to procure this dust that even Your wife Lakshmi was unable to obtain it, even after giving up all sense-pleasures and performing austerities for a very long time in conformity with the prescribed rules and regulations."
Just nearby are Krishna Kund and a sitting-place (baithak) of Shri Vallabhacharya. There is also a temple of goddess Lakshmi here.