Here's a video that explains how it works:
Essentially, by paying with Sezzle, customers login to their bank and pay the merchant from their bank account. Sezzle gives you 1% cash back every time you pay with Sezzle.
Merchants are usually charged 2.9%+30c of each transaction. Sezzle brings that cost down to 1.5%+15c by utilizing the bank sign-on technology. ACH (or paying through your bank) is much cheaper to process.