Shani Puja is to appease the planet Saturn. This is very useful & beneficial puja, since it's worship strengthens benefic Saturn & increases its positive influence and pacifies malefic effects of the planet & neutralizes its negative effect. Astroshastra recommend this for those having malefic Saturn or wrongly placed Saturn as per horoscope.
The planets are to propitiated against their evil influences, to ward off them, the Saturn Puja is done with faith to ward off all evils of Saturn as per the horoscope. The Puja is done by chanting the mantras of Lord Shani to appease him and ask for his blessings.
Shani (Saturn) is an indicator of longevity, misery, sorrow, old age and death, discipline, restriction, responsibility, delays, ambition, leadership and authority, humility, integrity, wisdom born of experience. Saturn is regarded as a planet of darkness which rules over the dark side of human nature, such as the conscience (awareness of right and wrong).
Puja of Saturn is regarded to be both a giver as well as destroyer. A person who sincerely prays to Shani is blessed not only with removal of the problems and worries, but a life that one desires. Shani Puja or worship of Saturn mitigates the hardships one will have to face during bad times. Shani Puja is also recommended to people who have Saade Sati of Shani in their horoscope or people having Mahadasa of Saturn.