The first number / letter combination (e.g. 5W) indicates how well the oil will flow to lubricate critical engine parts at low temperatures. The lower this number, the more easily the oil will help your engine to start in cold weather.
The second number (e.g. 30) indicates the oil's ability to lubricate the engine at high temperature. In this case, the higher the number the thicker the oil. A multi-grade oil, SAE 5W-30 in this example, satisfies the requirements of both cold start and high temperature viscosity grades.
So in a nut shell, you get a thinner oil that provides the protection of a thicker oil at 100 degrees by the use of chemical additives. The old manual I refer to is from Chevrolet 1941-46