People who belong to the Hindu faith, worship Lord Shiva on Mondays. Though they can pray to their favourite deity on any of the other days, Mondays are devoted to the worship of Lord Shiva. Monday is called Somwar in Hindi, and it means the day of the Moon (Som in Hindi means Moon). In simple words, Monday is controlled or governed by the Moon.
There's an interesting legend associated with Som (Moon) and Shiva. The Moon God (Chandra) married all the twenty-seven adopted daughters of King Daksha. They represented the twenty-seven Nakshatras or stars in the sky. Though he was married to 27 princesses, Chandra gave more attention to Rohini, and this enraged her sisters. Rohini's siblings complained to their father about Chandra's bias. Initially, Daksha requested Chandra not to do injustice to the rest of his daughters, but despite repeated warnings, when the latter turned a deaf year, the King cursed his son-in-law for his high-handedness. Daksha's curse started showing its effects after Chandra gradually started losing his glow and shrinking in size. Fearing that he would cease to exist, Chandra rushed to Lord Brahma for help, who then suggested he must pray to Lord Shiva.
Chandra offered his prayers to Lord Shiva until the latter was pleased by his devotion. But since the curse of Daksha had already shown its effects, Lord Shiva couldn't revoke it entirely but blessed Chandra the powers to retain his form gradually. Hence, the Full Moon (Purnima) appears approximately once in fifteen days after growing in size and then slowly shrinks until it disappears (Amavasya). And since Lord Shiva saved Chandra from losing his form, he is also known as Somnath. Moreover, he is also referred to as Chandra Shekhar because the crescent moon adorns his matted locks.
Therefore it is believed that those who worship Lord Shiva on Mondays, can rid themselves of all their troubles.