Markandeya, the son of the sage Markandu, had pleased Lord Shiva for a long life by doing severe penance in the month of Sawan itself. Yamraj, the god of death, also bowed down in front of the mantra powers received from Lord Shiva.
According to mythological belief, the sea was churned between the gods and the asuras in this month of Sawan. Lord Shankar had preserved the creation by absorbing it into the throat after the sea churned. But Mahadev's throat became Nilavarna due to poisoning. To reduce the effects of the poison, all the gods and goddesses offered him water. Therefore, offering water on Shivling has special significance. This is the reason why offering water to the naive in the month of Shravan gives a special benefit.
Another reason that Lord Shiva loves the month of Sawan is that Lord Shiva had descended to earth and visited his in-laws in the month of Sawan and was welcomed with Arghya and Jalabhishek there.
It is mentioned in 'Shivpuran' that Lord Shiva is water itself. Therefore, anointed with water, Bhole Baba fulfills every wish.
It is discussed in the scriptures that Lord Vishnu moves to Yoganidra in the month of Sawan. Therefore, this time is invaluable for all the devotees and sages. After Lord Vishnu goes into sleep, Lord Shiva takes up the responsibility of operating the universe. Therefore, Lord Shiva becomes the presiding deity of Saavn.