If a PlayStation 2 disc will not spin, the cause is most likely that the motor that powers the disc drive is broken, or it is not receiving power. Both of these problems can typically be repaired by replacing the disc drive.
While the PlayStation 2 has a durable disc drive compared to other systems, they are not impervious to damage, and they sometimes break. Because most consoles were produced more that 10 years ago, their disc drives are old and may be in need of replacement.
Disc drives have to spin the disc they contain, and they use a motor to do so. Over time, the motor can be damaged by dust or other contaminants, and some disc drives fail due to small manufacturing defects. It's possible to replace just the motor, but it's better to simply buy a new drive.
The power supply on a PlayStation 2 can also become damaged over time, and it might not deliver the power needed to use the disc drive. The cable connecting the power supply to the disc drive can also become damaged. Replacing the drive can fix the problems, but a faulty power supply may require purchasing a new system.