Reinstall Game Data
Try reinstalling the game data for the game you are attempting to play. Enter the "Game" menu and then go to "Game Data Utility." Select the game you are trying to play and then "Delete" the game data saved on the console. Put the disc in the tray again and try to reinstall the game data.
Inspect Cleanliness of Disk
Residue or other debris is often the culprit in disc performance. Pull the disc out of the tray and inspect it. If you need to clean the disc only use a soft cloth and wipe from the inside to the outside of the disc. If you rub in circles you are more likely to scratch the disc. Avoid getting fingerprints on the bottom of the disc by holding it by the outer rim. The PlayStation 3 is not designed to work with DVD cleaners, so do not put such a device into a console's disc tray.
Check Backwards Compatibility
If you have a PlayStation 2 disc in your console it may not work. Only the CECHA01, CECHB01 and CECHE01 models of the PlayStation 3 are backward compatible with those earlier game titles. Check the bottom of the console to see if you have the right model. You can't add this function by trying to modify your console at home, and tinkering with the PlayStation 3 will void your warranty. Not all PlayStation 2 discs work with the PlayStation 3 models that are backward compatible. Visit the PlayStation support website to see the list of titles that are.
Try Different Console
If you have access to a different PlayStation 3 you can try the disc in this console. If the disc works in the other PlayStation 3 yours likely needs repair. If you have a warranty with the retailer where you purchased the console take it there first. If not, visit the PlayStation support website for Sony support options.