Guild Wars 2

What exactly do these do? Do they have a greater chance at harvesting a larger yield (two or more per swing)? Do they have a greater chance at granting more swings at the node? Or do they have a greater chance at yielding unidentified dyes (plant nodes) or gemstones (sapling and ore nodes)? Thanks.

All of the above actually. They increase the chance of rare finds from any harvest node.

As far as I know, everything you said except more swings.