Sankat Mochan means the liberator from distress and is a popular title given to Hanuman. Legend has it that Hanuman was the given the title Sankat Mochan by Shani Bhagavan after Hanuman rescued him from Ravana’s prison.
Hanuman enters Lanka and starts searching for Mata Sita. Soon he hears cries from a dungeon. Hanuman finds Shani Bhagavan in the prison.
In the prison Shani was chained upside down like a bat and his face turned to the dark wall. Shani was tied in such a way so that his glance will not fall on anyone.
Hanuman breaks the chain and frees Shani. But Shani glance Hanuman during the process.
Naturally Shani should have caused hardships in the life of Hanuman. But Hanuman was not harmed by Shani because He was the devotee of Sri Ram.
It is believed that blue sapphire protects people against Saturn’s influence, but since blue-skinned Sri Ram is the sapphire of sapphires, his devotees are safe from Shani. And Hanuman is the greatest devotee of Sri Ram
Shani also gives the boon that in future devotees of Hanuman will not be troubled by Him. For rescuing him from distress, Shani gives Hanuman the title Sankat Mochan.