If your computer's optical disc drive (the drive that reads either CDs or DVDs) won't read a particular disc that you insert, the problem could be coming from a few different directions. There could be an issue with your computer's software that operates the drive, with the hardware on the inside of the drive or with the disc itself. Only troubleshooting will allow you to find the real cause of the issue.
Roll back the drive's device driver using the Device Manager. The Device Manager is accessible through the control panel. You can roll back the device driver by right-clicking the icon for the drive and entering into the "Properties" window. Once opened, click "Driver" and then "Roll Back Driver" from the "Properties" window. This will correct issues that the drive was experiencing due to a faulty or incompatible driver.
Clean out the inside of the drive. Most electronics retailers offer optical disc drive cleaning kits. These kits will carefully clean the dust and dirt on the component on the inside of your drive known as the lens. If this lens is dirty, it won't be able to properly read the data contained on CDs or DVDs.
Make sure that the type of disc you're trying to play is a format that your drive can actually read. Not all optical disc drives are capable of reading every type of optical discs. A DVD drive can read both CDs and DVDs, for example, but a CD drive can only read CDs and not DVDs. Likewise, certain types of DVD drives cannot read "dual layer" discs, while others can. Consult your drive's instruction manual to see exactly what types of discs the drive can play.