Parallel linesIn the plane, two lines that are not parallel are secant (or transversal). That's not the case in space. For example the line on the right of your computer screen (vertical), and the line on the left of your desk (horizontal) are neither secant nor parallel.
In this cube, the blue lines are parallel, the yellow lines are neither parallel nor secant.
Orthogonal linesTwo lines are orthogonal if there exists a line which is parallel to the first one and perpendicular to the second one.
In this cube, the two red lines are orthogonal because the horizontal one and the green line are perpendicular.
Intersections in spaceIt's easy to imagine that if a line is not parallel to a plane, then the intersection between the line and the plane is a point. And if two planes are not parallel, then their intersection is a line. The roof theorem mentions that if two planes that are not parallel pass through two parallel lines, then the two parallel lines are parallel to the intersection line of the two planes (it draws the roof of a house).
See also : geometry on fmaths.com