So i've played about 50 hours of Oblivion, that's long or me lol, and I just noticed when looking at an items stats, there's value, weight, then a sword, then how much health it has left... what's the sword? is it damage?

That′s how much damage the weapon does.

Yes.

And it's dynamic. The damage will go up if your skill in the weapon type does. Same with your attribute that governs the skill (strength for melee, agility for bow). Damage can also go up and down a bit based on how fully repaired the weapon is.