Basically, you loan money to a small business in a developing ("poor") country, they use it to invest in their business, they get rich, and you get your money back. With the interest you get in return, soon everyone will be driving Cadillacs. This screenshot from the Kiva website sums it up better than I ever could:
Per Kiva's FAQs, you will receive no interest on your loan. The only compensation you receive is the satisfaction of helping those in need.1
1Some people would say this has "priceless" value.2
2Still others might point out that, technically, this has "worthless" value.