Jack's sword is the only thing that can hurt Aku
The gods Odin, Ra, and Vishnu forged the sword for Jack's father and imbued it with cosmic energies from amongst the stars. Not only is it the only weapon on the planet that can defeat Aku, it's inextricably linked to Jack and his mission to vanquish evil. That's why it disappeared for so long while Jack had lost his sense of balance.
The IDW Samurai Jack comic book, published between 2013 and 2015 for 21 issues, also featured a storyline written by Jim Zub called "Samurai Jack and the Quest of the Broken Blade" -- where Jack had to contend with having broken his sword. It actually ended in a similar fashion as I pointed out when this season started, with the power of the gods manifesting itself in the form of a new sword. Genndy Tartakovsky, creator of Samurai Jack, doesn't consider the comics canon, but this reveal happened in much the same way.