What specifically is a Category B insurance loss? My friends were involved recently in an accident, not majorly and not their fault, but they have been told their car is Category B. Also, does this affect their insurance?

In the UK the insurance loss categories used by insurance companies include:

Category A - Severely damaged so much so that the whole vehicle cannot be resold but must be taken off the road and crushed. There are no serviceable parts. The DVLA will require a Notification of Destruction for the vehicle.

Category B - The Vehicle as a whole may not be resold or returned to road but parts may be sold. The vehicle is damaged beyond repair usually due to major structural damage. The DVLA will require a Notification of Destruction but parts are allowed to be removed and sold first.

Category C - Repairable salvage. Significant damage to the vehicle so much so the cost of the repair exceeds book value. It can be sold for repair but must have a VIC inspection before returning to the road.

Category D - Repairable salvage. Vehicle has minimal, probably non-structural damage. May have been economic to repair, but insurer does not want to. Often this is due to the vehicle being stolen and recovered after the claim has been paid to the insured. Or the parts to repair the vehicle are difficult to find. Does not need VIC inspection to return back to the roadway but notification will remain on the vehicle history check.

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Category X - Repairable vehicle with minor damage. It has been part of an insurance claim but was lightly damaged and required minimal repairs. This is not recorded with the DVLA so would not appear on a Vehicle Data Check.

According to the insurance loss category listing a Category B loss is quite serious so much so that the vehicle cannot be repaired but can only be sold for parts.

As for insurance, since your friend was not at fault (thus the insurance claim should go through the at-fault party's insurance) then the friend's insurance no claims bonus should not be affected. To find out for certain if their rates will be affected in any other way, he or she will need to discuss the rating system of their insurance provider with their insurance agent though.