The two main purposes of wrapping the Air Conditioning Insulation around the copper pipe:
1. It acts as a protective layer for the copper pipe.
2. It helps to absorb condense water from the copper pipe. When the air-conditioner is running, the compressor will starts to compress the gas to liquid which causes the copper pipe to be cold which form condensation. Just image a cup of cold beer, the condense water form outside of the cup due to the cold beer. This is what happening to the copper pipe.
The insulation act like a sponge which absorb the condense water forms on the copper pipe. When times goes by, the insulation could not hold any more water. The copper pipe that is located right behind the fan coil unit will starts to leak whenever you switch ON your air conditioner. It will starts to drip water when it reaches its water capacity limit.