Multi-weight oils (such as 10W-30) are a new invention made possible by adding polymers to oil. The polymers allow the oil to have different weights at different temperatures. The first number indicates the viscosity of the oil at a cold temperature, while the second number indicates the viscosity at operating temperature. This page from the Sci.Electronics.Repair FAQ offers the following very interesting description of how the polymers work:

At cold temperatures, the polymers are coiled up and allow the oil to flow as their low numbers indicate. As the oil warms up, the polymers begin to unwind into long chains that prevent the oil from thinning as much as it normally would. The result is that at 100 degrees C, the oil has thinned only as much as the higher viscosity number indicates. Another way of looking at multi-vis oils is to think of a 20W-50 as a 20 weight oil that will not thin more than a 50 weight would when hot.