The tradition of offering mustard oil to Lord Shani on Saturdays has deep roots in Hindu mythology and holds significant spiritual meaning. The story behind this practice is linked to an incident involving Lord Hanuman and Lord Shani.

While Hanuman was busy serving Lord Rama, he crossed paths with Shani, who caused trouble and disrupted his work. Despite Hanuman's warnings, Shani remained stubborn. In a fit of anger, Hanuman grabbed Shani by the tail and continued his work, causing Shani to suffer injuries.

After finishing his service to Lord Rama, Hanuman realized his mistake and freed Shani from his captivity. Shani, grateful for Hanuman's help and regretting their earlier clash, blessed Hanuman's followers and announced that anyone who offered mustard oil to him on Saturdays would receive his special blessings.

This act of applying mustard oil symbolizes respect and devotion to Shani. The oil was used to heal Shani's wounds, and since then, it became customary to anoint Lord Shani with mustard oil every Saturday. 

This ritual is believed to bring blessings, remove obstacles, and offer protection. It teaches values like humility, forgiveness, and the power of devotion, making the offering an essential part of Shani worship.