The Xbox 360's power button is surrounded by a ring that lights in red if ever a problem occurs. The ring is divided into 4 quadrants so that some or all of the lights can flash to indicate various problems. If all four ring flashes, the problem is related to the AV cable.
Two lights flashing is more than likely a minor problem with your system. This can be resolved by simply letting the system cool down.
If 3 lights flash, you are dealing with the dreaded “Red Ring of Death” problem caused by heat issues and mostly manufacturing defects requiring you to take it to a shop for repairs or perform the Xbox 360 repair yourself.
If you only see the bottom right light flashing, a lot of different things can be going on which can be explained in-depth.
The problem isn't however as lethal as the Xbox 360 3 red lights so don't panic. Once you notice the bottom right light flashing, look at your screen and you should see an error code that begins with the letter “E”. Below is an explanation of some of these codes.
Hard Disk Errors (E69 & E79)
Error codes E69 and E79 are common for players that prefer playing their games stored on the hard disk. The problem can be a loose connection between the hard disk and the Xbox 360 internal component or the hard disk could be damaged.
To make sure, take out the hard disk and see if the system works. If it doesn't work, test it on a computer and see if you can recover it using some hard disk utilities.
DVD Drive Errors (E64 – E66)
Any of these three error codes can indicate that the firmware of the DVD drive doesn't match the dashboard or the firmware chip is missing. If the firmware is okay, the problem can be physical and may need replacement.
Solving firmware issues require you to upgrade the lower version to make it equal with the higher version. So you might need to upgrade either the firmware or the dashboard and your DVD drive should work fine.
As long as you have the original drive that came with the purchase of the system you will not likely have this problem.
NAND Flash Errors (E72 and E80)
Although the E72 and E80 are both related to the NAND flash, the errors are quite different. The E72 represents a general problem and should be checked by support while the E80 indicates the wrong LDV version of the NAND flash.
Other Error Codes
There are other error codes that are not very common such as the E76 code, which is related to Ethernet problems, and the more popular E74 code, which is related to the GPU or AV cable.
If you are unsure on what action to take, check out Microsoft's support site for official code information and search for the error code to see a list of solutions that can get your Xbox back to its working state.