These weapons are very similar to sais, except that they have only one side prong. They are used very similarly and were very popular with police and guards in ancient Japan. They were especially useful to Royal Guardsmen as it was illegal to carry a bladed weapon on palace grounds. Thus, this bladeless weapon was invaluable to the guards and became a symbol of their office.
In several episodes, two Jitte can be seen sticking out/stabbed into of one of the turtles' practice dummies. It is still unknown who will use it in the series, or if it'll be ever used.
The name of these short iron bars translates to "ten hands," because that's how strong they are.