When you first plug in your Xbox 360 and turn it on, it is set to one specific region. This means that the console is programmed to only allow you to play games you've purchased from the same part of the world where you bought your Xbox 360. This is done to combat rampant piracy around the world. You can, however, take a few steps to make your Xbox 360 region free, which means it will be able to play games purchased anywhere on the planet.
Download new firmware. Firmware is the main computer program that operates your Xbox 360. It tells your console how to operate, and it is what is keeping your Xbox 360 from being region free. You can find user-created firmware updates in various places online. These are unofficial releases that have no association with Microsoft, and they will void any kind of warranty you have.
Burn your new firmware to a CD or DVD. Open whatever burning software you use and burn the files you've downloaded, just like any other file.
Put the firmware CD or DVD you've just made in the Xbox 360's disc tray.
Open the disc and execute the files once your Xbox 360 recognises the disc. This will flash your Xbox 360, which is a technical way of saying it will change your firmware from the version it came with to the new version you've downloaded.
Restart your Xbox 360 to finalise installation of the new firmware. When it boots back up, you can play games from any region of the world, and you are no longer limited to the region you purchased the console in.