It is said that the blue and red fraction of VIBGYOR is mainly used for photosynthesis. Can somebody explain why this is so?
The there are two main types of chlorophyll involved in photosynthesis, chlorophyll a and chlorophyll b. Each one is effective at absorbing energy in the form of light at a different frequency - one absorbs red light best, the other absorbs blue light best. The two are also used in two different photosystems, I and II, which have different functions, but the end result for both is that the chlorophyll gains energy for the plant to use.
The rest of the spectrum isn't used because plants haven't evolved proteins that utilize the rest of the spectrum; what they have is apparently sufficient for their needs.
This is a good resource to get a better understanding of the details of photosynthesis, and honestly Wikipedia doesn't do a bad job of explaining it.