The "before" was applying for a store-branded credit card at the point of sale, which evaluated your credit risk and (potentially) extended you a revolving credit line equal to what the lender deemed was your appropriate borrowing capacity, potentially far in excess of your purchase amount.

Affirm is just a "micro-transaction" take on that very large and lucrative market. They extend a fixed term, one-time line of credit equal to your transaction amount and no more. Want to use Affirm for another transaction? That'll be an entirely independent line of credit for that transaction, subject to its own application/approval process.

There are a lot of somewhat novel aspects to Affirm's approach, but the core premise of Affirm itself one of them. For better or worse, making it easy for consumers to over-extend themselves by dangling a credit line at the point of sale was widespread and lucrative long before Affirm entered the market.