As the jitte is tipped with Seastone, it can be used to nullify Devil Fruit powers simply by contact. Smoker uses this to his advantage to strike such opponents, as well as to stop them by sapping them of their powers and mobility. He uses it in conjunction with his Moku Moku no Mi powers to get close to his opponents in order to make his strike land. Because of its composition, the jitte does not transform into smoke along with Smoker.
Smoker can also imbue the jitte with Busoshoku Haki, turning it darker in color. This makes it much harder and allows him to strike with much more force.
While Smoker does not name any attacks with his Jitte in the anime or manga, he showed one in the games.
Jitte Ranbu (十手乱舞,Jitte Ranbu?, literally meaning "Jitte Dance"): Smoker swings the Jitte multiple times for horizontal strikes, hitting the enemy into the air, before using his smoke powers to circle back around and deliver a final blow that knocks multiple foes far back. This was shown in One Piece: Pirate Warriors 3.
The weapon was effortlessly destroyed by Boa Hancock when she kicked it to pieces after petrifying it. Two years after its destruction, Smoker is seen wielding the staff once again, apparently repaired or replaced by the one seen on the wall of his office when he is first seen. However, it was once again destroyed by Vergo's Oni Take.
In the manga the handle is pure white and the body a light color, while in the anime it was first introduced with a metallic dark gray body and a brown hilt. This was later correct after the timeskip, in Episode 572, to match the manga color scheme, in which the new jitte is now silver-white and has a white hilt wrapping.
The jitte (also known as a jutte, both meaning "Ten Hand") is a weapon used by Japanese law enforcers, which fits Smoker's status as a Marine officer perfectly. The hook on a jitte is normally meant to help disarming an opponent, while the truncheon part is used to subdue the criminal.
A shaku is a measurement unit in Japan, one shaku being 10/33 meters. Based on the name (seven shaku), the jitte is 2.12 meters in length.
It is probable that Smoker either owns more than one jitte, or has authority to order a new one, seeing how his jitte got broken at the Battle of Marineford and was later replaced.