Upvote:5
The significance of this act was its importance in the Hamilton-Jefferson debate. Basically, Hamilton's idea was that of a large, strong, federal government. Jefferson and his supporters favored a weaker, de-centralized, and (in most cases) a state based government. Hamilton won this round by "federalizing" what had been Revolutionary war (and subsequent) debt.
The assumption of the states' debt meant that there would be one large centralized "national" debt, instead of 13 smaller ones. It was much easier for lenders, foreign as well as domestic, to monitor and deal with one federal debt, which had earlier been incurred by the states mainly to fight the Revolution, and to operate until the "United States" got going.
Yes, the states later incurred their own state debts, but for local matters, (usually) funded by "local" citizens. These debts were much smaller than the "national" debt that had been undertaken to fight the Revolution. By repaying the national debt promptly and in full, America established the credit it needed to fight future wars and to deal with other national emergencies.
There was one other thing. The federal responsibility to pay off the central debt was accompanied its control over most revenue sources, mainly tariffs and excise taxes (income taxes were permanently established in 1913, over a century later).