The numbers in an oil's viscosity grade represent the oil's thickness at different temperatures. The lower the first number, the thinner the oil is at low temperatures. The higher the second number, the thicker the oil is at high temperatures.
5w30 oil is thinner at low temperatures than 10w30 oil. This is important for engines that are cold. When an engine is cold, the oil needs to be thin enough to flow easily through the engine and lubricate all of the moving parts. If the oil is too thick, it won't flow easily and the engine won't be properly lubricated.
10w30 oil is thicker at high temperatures than 5w30 oil. This is important for engines that are running hot. When an engine is hot, the oil needs to be thick enough to stay in place and protect the moving parts from wear and tear. If the oil is too thin, it will become too fluid and won't be able to provide adequate protection.
Using the wrong viscosity oil can damage your engine. If the oil is too thin, it won't be able to protect the engine from wear and tear. If the oil is too thick, it won't flow easily and the engine won't be properly lubricated.
It's always best to use the oil that is recommended by your vehicle manufacturer. In the case of the 2003 Pontiac Grand AM GT V-6, the recommended oil is 5w30.