Cause
The three flashing red lights around the power button of the Xbox 360 indicate that an internal problem is occurring, such as with the hardware of the machine. It is known as "The Red Ring of Doom," or by other similar names. If four lights are flashing red, this is an indication that the machine is not plugged in correctly, or that the power supply is not functioning.
Home Solution
Before you call Microsoft, you can do a few things to rule out some common issues. First, make sure all the wires are plugged into the appropriate regions, and that they are fully inserted. Then, check the power supply box (the box connected to the wire that plugs into the outlet). If there is a red light or no light at all on the power supply box, that is an indication that the power supply box is not functioning. Try plugging the machine into a different outlet, as sometimes a tripped circuit breaker or a faulty outlet might be the cause of the malfunction, rather than improperly connected wires. Sometimes the power supply box may overheat and you can also try letting it cool off for a few minutes. If you have tried these solutions without success, visit the Microsoft website and order a replacement power supply box (see Resources).
Further Actions
If the three flashing lights persist, and checking the wiring, power supply box and changing outlets has not remedied the problem, send your Xbox 360 to Microsoft for repairs. See resources for a link to start an Online Repair Request, which Microsoft recommends for convenience. The Microsoft Xbox Service Center says that repairs will typically take "14 to 21 days," but it is free as long as the machine is still under warranty.