You mean why WAS the revolutionary tribunal so powerful? Well, they had popular opinion on their side as well as a hundred percent belief that they were in the right. Jean-Paul Marat held sway in that court, examining whether a noble or sympathiser should be relieved of his property or his head.
It is often said that he was a psychopath or worse, but his identification with the struggle of the majority classes owning no property, few rights, his work for social equality made for a new invigorated France, a more moral one.
The power of the tribune was perhaps a sign to the popular mass that action was at last being taken against those who had oppressed them, de-enfranchised them for generations.