There are actually 2 answers to this question. First, if they are in the same plane they are parallel. Second, if they are in different planes they are skew.
The point of intersection.
point
A point.
If the lines are identical, then the whole lines. If not they can either not meet at all or at a single point: the point of intersection.
It is usually called an intersection or an intersection point.
point I believe the word you're looking for is "intersection". Two non-parallel lines that lie in the same plane will have one point in common where they cross, and that point is the intersection.
intersection
point
Intersection.
a point
The point where two or more lines meet is the intersection.
point of intersection