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.
intersection
point
Intersection.
a point
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.
The point where two or more lines meet is the intersection.
point of intersection