You can certainly build your characters however you like, but the idea is that, as a dominator, you lock down enemies and make them your playthings; You may want to do your damage from range, or you may want to take the risk, (albeit lessened thanks to your control abilities), to close to melee range and deal even more damage.
In the broadest sense, what you are "manipulating" is the element or type of ability associated with the set - fire, ice, martial arts, etc. Those powers are there to compliment your ranged blast attacks and also to compensate for when the enemy closes in.
A Corruptor's secondary set if buff/support. The sets having names like "Nature Affinity" is merely there for flavor. If you want to be more literal, it is simply an area your character happens to have a talent for.