Because concrete naturally breathes with the time of the year, retaining and evaporating moisture over its lifespan, it is not a sub-floor you can install wood directly on top of. Instead, a layer of plastic must be used to insulate the wood from the moisture in the slab. After that, a floating installation can be put on top of the plastic and slab, resulting in a finished hardwood floor.
Although concrete board is similar to concrete slabs in that it is a cementititous product, it is generally reserved for ceramic tile installations. If you are performing a remodel, though, you will sometimes need to run hardwood over concrete board sections of a floor. It is similar to slabs in its makeup, but concrete board evaporates moisture at a much more rapid rate, which means plastic isn’t necessary.
If you still think you want to include a moisture barrier, just to be safe, you can use felt paper instead of plastic sheeting on top of the concrete board underlayment. For extra protection you can run the barrier across the entire floor just to give the wood one more layer of insurance. You can also use plastic sheeting in this case -- but it is really overkill.
Because cement board is a ceramic tile or natural stone underlayment designed for use with those products, it is not something that was created for use with wood. Although you can nail down hardwood floors to concrete boards, they are harder to drive than when the sub-floor consists of plywood. For this reason floating floors are usually used above concrete or concrete board floors because they are much simpler.