In SotN...
STR is "strength". It determines your basic attack power before you add the fixed number of points that get added by equipped weapons. Your STR + the weapon's attack power = your attack power with the weapon equipped.
CON is "constitution". It determines your basic defense power before you add armor. A "constitution" rating frequently affects thing like poison resistance in other games, but I'm not sure if it did that in SotN.
INT is "intelligence". It determines your magical attack power (damage also depends on the power of the spell being used). It might also affect magic resistance, or maybe that's just covered by the defense points.
LCK is "luck". It determines how often you get "critical hits", and how often enemies drop items. It may also affect how often and widely you stray from the basic "HP loss = attack power - defense power" formula.
Dawn of Sorrow probably works in a very similar if not identical manner. It is kind of odd that the DoS instructions explain the abbreviations, but don't take it any farther. I guess they just assumed everyone already knew these things.