Yes, you have to actively USE Concentration to raise your Hammer damage.
Vigor and Blessed Aim are "synergy" abilities. When you add hard Skill Points into them, your Blessed Hammer damage will go up. This is different from using Concentration. Concentration must be your active Aura (on right-click) to raise the damage of your BHs. "Synergies" in general will raise the damage of the skill they synergize. (Some of them increase the duration of some effects, but this doesn't apply to BH.)
Concentration is an Aura. When you have it on your right-click, that Aura is active for your Paladin. It does what it says. It is the only Aura that raises Blessed Hammer damage while active, and works at half the listed effectiveness. (The reason it works at half is because it's supposed to be an Aura to aide physical Paladins. Why Conc raises BH damage, which is a magical spell, is a story all its own.)
In simpler terms...
Vigor and Blessed Aim are "synergy" abilities for Blessed Hammer. If you put points into them, your Blessed Hammer damage goes up (as listed, 14% per point). You don't have to do anything else to get extra damage. "Synergies" work automatically and you'll always have that extra damage once you put the Skill Points into them.
Concentration is the Aura you want active to raise the damage of your Blessed Hammers. It will raise the damage of them by 50% of the listed value. (i.e. If your Concentration aura says "adds +100%" damage, Blessed Hammer with receive a 50% total damage boost.)
Boosting synergies, or Concentration, is a good way to raise the damage of your BH without making BH itself cost more mana. However, it also doesn't add as much damage as sticking a point into Blessed Hammer itself. Until you hit the Level 80's (where you can max BH, Conc, and both synergies), strike a good balance of splitting your Skill Points between your aura, synergies, and just Blessed Hammer itself. I suggest dumping a few (say, 5) points into BH itself to get some cold, hard damage going and then splitting the rest between Concentration and the synergies (Vigor and Blessed Aim). If you're confident in your mana level or you don't mind drinking blues a little more often dump your next Skill Point into Blessed Hammer itself, as you'll get a better damage boost by dumping your points straight into the skill.
How much more powerful? 8) If you're cruising now, you'll really cruise through Nightmare. Hell difficulty may bump you down a bit, but that's just because all the monsters suddenly get a ridiculous boost in power. You can go from man-handling Lister and co. in NM to being crushed by a Unique Quill Rat in Hell Blood Moor. But that's okay, because after a few more levels you'll start dominating again. Blessed Hammer just gets more and more powerful as time goes on and levels rise...