The festival of Mahashivratri is celebrated on 14th day of Krishna Paksha of the month of Phalgun, according to Hindu calendar. According to the English calendar this falls somewhere in the month of February or March.
Maha means huge, Shiva means auspiciousness and Ratri means night.
According to Puranas, during the time of Samudra Manthan a pot of poison came out from the ocean. Both, Gods and demons were frightened and they went to Lord Shiva for help. Lord Shiva drank the poison in order to save the world. However, he did not swallow it but held it in his throat. Since the poison turned his throat blue, he is known as ‘Neelkantha’ after that. It is believed that Mahashivratri was the day when all this happened and so people celebrate it by worshipping Lord Shiva.
Lord Shiva was formless until the night of Mahashivratri when he appeared in the form of huge Ling. This was actually to end the ego clash between Lord Vishnu and Lord Brahma. The Ling is said to be extremely huge and neither Lord Vishnu nor Lord Brahma could find the end or beginning of this Ling. From that day onwards people worshipped Ling as Lord Shiva and celebrated Mahashivratri every year.