The local microlending institution charges interest to the borrower and keeps it for their own profit and to cover operating costs. The borrowers can default but most don't. So you should treat it as a donation you're willing to walk away from. I sense that most people treat it as a donation, and then just continually recycle the money to new borrowers.
I have some reservations. The interest charged to borrowers often seems way to high, and kiva makes it a bit labor intensive to check on the interest rate charged by the local microlending institution (the best proxy for this is "portfolio yield" in the lender's profile). My personal preference is to target microlenders with low portfolio yields. This makes it more likely that the borrower isn't just paying off interest without accruing any equity from their hard work.
But, it's an imperfect solution in an imperfect world and I like feeling like my money isn't just covering some bloated bureaucratic administrative salaries of some development non-profit and is actually going directly to third worlders trying to better themselves through work.