It will amp up the damage noticeably, as well as stat bonuses, evasion ratings, and defense
Think of enchanting like fusing items - they grow in potency, but they don't compound DFO Gold exponentially (meaning two +1's into a +2 won't do double the damage) but it will amp up the damage noticeably, as well as stat bonuses, evasion ratings, and defense (such as on armor).
I recommend enchanting over buying whole new sets, as constantly gearing into + 0's (normal items) doesn't always make it worth spending the money - just keep compounding on the armor. Heck, some of my frontline tanks at 62 are using +8 rakshasa stuff (level 25). Enchanting is very handy for this!
Next, we'll talk about Atlantica Enhancing.
Atlantica Enhancing is different from Atlantica Enchanting insofar as you do not need an equivalent sacrificial item to enchant it, but with enhancing comes a 50% risk (I've heard it was lessened, but I'm skeptical) of failing and breaking the item.
Enhancing comes from Vulcan’s in Rome's Bazaar district - but the stones you need to Enhance are different, and are even called so (weapon enhance stone, armor enhance stone, accessory enhance stone).
Note that if you do not have Rome's map information, there golden arches on the right hand side of the screen denoting Rome's districts - Plaza, Bazaar, etc. Vulcan-us is in the bazaar, hang a right after you teleport in.