Apologies if this sounds dumb, but what does buying up debt mean in the context of ASOIAF? I believe Littlefinger mentions he does this to Vale Lords in Feast.

It means the same thing as it does in our world: you find the original creditors of a given person and you offer them money (preferably less than the full value of the debt) to hand over the right to repayment for the original loan. And then you either try to collect the debt or you threaten to in order to get the debtor to do what you want.