CDs work on the principle of reflection of light. CD drives have a built in laser that is used to read data. When laser is focused on to the CD the beam get reflected to a point when there is some data on that are i.e. 0 or 1 the points where light beam lands back is different which symbolizes the bit value.

When something on the CD breaks the path of the laser light, something like dust particle or something else like a FINGER PRINT!!!. Finger prints are nothing but natural oil from skin that sticks to the surface in contact with the skin in a pattern of skin cells. This oil or say fingerprint helps in refraction of light and loss of data to the reading source i.e. laser.

When CDs don't run the reason is because something is interrupting the laser to read the shinny side of the CD. But I have important data what should I do now?

Most of the times it is because of dust or fingerprints, you need to clean the CD.
You can clean your CDs with plain water or a bit soapy water. And it is better to clean the CDs after some time. But this doesn't mean you should start putting your CDs in dishwasher or washing machine every week.

All you need to do is to wipe the shinny side of the CD with a clean moist cloth and try running it again make sure the CD is dry before you run it.

People say about using all different sorts of things to clean CDs like toothpastes, wax polish etc. but I would recommend you to buy some CD cleaning kit. But if you still want to go try, do let me know the results.

And one thing I must add is that DVD work on the same principle and are bit more sensitive to dust and fingerprints. You can also use the above mentioned procedure for DVDs. But you need to be careful with DVDs