Click Intersection when the command prompt requests a point to use this modifier.
When you select INTERSECTION OF you are prompted for a "Intersection of 1st entity:". If the pick box contains an intersection, it will automatically be selected. If you select an entity, but do not enclose an intersection in the pick box, you will see the "2nd entity": prompt. Select a point on another entity and CC3 will automatically find their (nearest) intersection.
Two selected entities don't actually have to cross. CC3 will calculate the mathematical intersection of the entities where it is possible. It is not possible to calculate an intersection beyond the end of smooth entities, as there is no unique point.
Text equivalent: INT (or press function key F6)