After referring to some good online resources such this, I know why we shouldn't transport it laying down.
Compressor is filled with oil which is critical to its operation. In the normal upright position gravity keeps the oil in the compressor. When we lay the refrigerator flat, some of the oil can leave the compressor and go into the cooling lines. The oil is a thick viscous fluid and can clog the cooling lines thus hampering the refrigerator's ability to cool. Lack of oil in the compressor can also damage the compressor.
If we must lay the fridge down, it is better not to lay it 100% flat, but rather to keep an angle so gravity keeps the oil in the compressor.
If it has lied down flat for some time, then wait at least 24 hours with the refrigerator in the normal upright position before turning it on.
This will allow sufficient time for oil that may have gotten into the cooling lines to flow back into the compressor.