Strange that there's a distinct lack of information yet some general assumptions are made.
In any case, answering the original question, if you want to play "backup" (because pirate is taboo and makes it sounds like you don't care about the people who make the game and just expect free entertainment of the most supreme quality like a conceited so-and-so) games, you just need to flash a new custom firmware onto the DVD drive of the Xbox that will be able to read burnt/backed up games. If it's Hitachi, Samsung or BenQ, it's a fairly easy and straightforward process. If it's a LiteOn, 7 series needs a probe/spear tool to flash, 8 v1 can be done easily, 8v2 and 9 series LiteOns are NOW FLASHABLE (in contrast to the above post) but the process is more complicated than you are likely to bother trying with (involves a solder iron, some wires, and I think 2 diodes).
The newer the console (you can tell by the MFR on the sticker on the back), especially if it's after June '09, the more annoying it will be to flash it, but once it is flashed, it will likely be able to play all games you want just by sticking the DVD in. Also all current custom firmwares are detectable by M$ so if you connect to LIVE at any point with a flashed drive, you WILL be banned (or at least it seems that way after over a million got banned recently).
To unflash it, unlike what was mentioned before, you don't need the DVD key but rather the original unaltered firmware. If you have bought it pre-flashed (as someone assumed above), then you will be very lucky if they actually provided it to you as most don't bother. If you did it yourself using JungleFlasher, you'll likely have a file like "BenQ-OFW.bin" (assuming its a BenQ drive) hanging around somewhere. That's what you need, and if you have it somewhere, you can unflash the drive using JungleFlasher and a tutorial. If you don't have it, you can't unflash it. If you have not yet flashed your drive, then obviously you won't be able to play backup DVDs yet.
Bottom line, to play a backup game, stick in the backup DVD into the drive and see if it runs (if it does, problem solved). If it doesn't, try another to check if it's the disk. If it still doesn't run, try any old movie DVD or audio CD to check if it's the drive. If nothing seems wrong but it won't play backup games, then you'll need to go about opening it up and flashing the drive. If you're still having trouble after this, you can read the tutorials on this site, or google up more tutorials to try, or just post another question here. Some people don't like people who don't bother trying to use the search bar or google search engine, some will be more patient and just answer your questions over and over. EDIT: When asking a question though, it probably helps to actually tell us more information than "I have my console, I have my pirated games, what now?"