According to Ashish Srivastava's answer on What's the significance of worshiping Shiva in the month of Shravan?:
Later in Naimisharanya, Shukdev told - In the month of Sawan only Shiva consumed poison. The Samudra Manthan is a very important episode as per the Puranas. The churning of the milky ocean, i.e. Samudra Manthan in search of the amrit, took place during the month of Shravan. During the churning, 14 different rubies emerged from the ocean. Thirteen rubies were divided among the devas and the asuras, however, Halahal, the 14th ruby remained untouched as it was the deadliest poison which could destroy the whole universe and every living being. Lord Shiva drank the Halahal and stored the poison in his throat. Due to the impact of the poison, his throat turned blue and he came to be called Neelkantha. Since this was the time when Shiva saved everyone from dying, he is worshipped with priority in the month of Sawan only.
Such was the impact of the poison that Lord Shiva wore a crescent moon on his head and all the devas started offering water from the holy river of Ganges to lord Shiva to reduce the effects of the poison. Both these events took place in the Shravan Maas and therefore, it is considered very auspicious to offer holy Ganga water to Lord Shiva in this month.
After consuming poison, Lord Shiva's body temperature had raised. After seeing this, gods have started to pour water and offered belpatra to him. Indra ordered clouds to rain over that place.
Science have proved that during the rainy season, milk contains bacteria, which could not be consumed by human. Otherwise it results into diseases. So it can be poured into shivling. Philosophically, by offering milk we pray for good qualities like milk. Similarly offering water represents that surrender your life to the lotus feet of Shiva. Offering bhang denotes about to take our negative qualities.