This is known as the (in)famous Red Ring of Death. This is almost always caused by overheating. Simply cleaning out all of the air vents, fan, and so on with some compressed air should resolve the issue. Note that the 360 works best when not in an enclosed space, like some entertainment stands have (e.g. a glass door). There needs to be good air flow around the entire system for it to avoid overheating.
If you cleaned out all the dust and other obstructions, but still experience this problem, you can fix it by increasing the thermal dissipation by using a simple trick that's been circulated on youtube involving pennies, electrical tape, and a T9 screwdriver, or by using a towel. Alternatively, if you don't feel like using "hacks," you can get a RROD kit that will allow you to fix the problem permanently. Finally, you might just try to find a service that will fix it for you. For example, near where I live, there's a game repair shop that can fix issues like this for a nominal fee.