A cross-class skill is a skill that is at best tangentially related to the role of a given class, making it harder for that class to learn that skill. The opposite of a cross-class skill is a class skill. The difference between "class" and "cross-class" is determined based on the class being advanced during level-up.
It takes two skill points to add a rank in a cross-class skill. (Unlike pencil-and-paper D&D, Neverwinter Nights does not track half ranks.) The highest the ranks in a cross-class skill can be raised to is (character level + 3)/2, rounded down (which is half of the limit for class skills). A cross-class skill may be higher than this limit if it was raised as a class skill earlier, but it may not be raised higher during the current level-up.