The custom of carrying holy water from Sultanganj on Kanwar and offering to it Shiva started in the Treta Yuga - the silver age of Hindu mythology. Lord Rama had carried the holy ganges water from Sultanganj in a kanwar and offered to Lord Shiva at Babadham.
The legend says that when the churning of oceans - Samudra Manthan - took place in the month of Shravan, fourteen different types of rubies came out. Thirteen of these were distributed amongst the deamons, except Halahal (poison). Lord Shiva drank the Halahal and stored it in his throat. Hence the name Neelkantha (meaning blue throat) is attributed to Shiva.
To reduce the strong effect of poison, Lord Shiva wore the crescent moon on his head. All the Gods, thereafter started offering the Ganges water to Lord Shiva to make lessen the effect of poison.
Since, this happened in the month of Shravan, since then the Shiva devotees offer the Ganges water in this month.