A long time ago, in a galaxy far, far away...
There was a Mandalorian that was also a Jedi. His name was Tarre Vizla. This was kind of a big deal because Jedi and Mandalorians were pretty much enemies. In fact, much of the Mandalorian weaponry and gadgets were designed so they could counter the Jedi's powers. Anyway, he created his lightsaber and it was the Darksaber. Many years after his death, the Darksaber became a symbol of the ruler of Mandalore. Whoever wielded it was the rightful ruler of the Mandalorians.
Now, I'm only a medium SW nerd, so I might be missing some details. But this is kind of the basics.
So technically, Moff Giddeon would be the ruler of Mandalore. Of course, this doesn't mean that no one will challenge you. It's not like King Arthur where whoever has it is the King and no one challenges his rule.
The Darksaber is the most prized possession of the Mandalorians, along with Beskar. But I would say that as big a deal Beskar is, the Darksaber is a hundred times more so.