Finite lines are lines which have distinct endpoints. Geometry methods such as line from two points create finite lines using the endpoints you specify. Infinite lines do not have end points and therefore go on forever. No matter how much you zoom or pan, you never see the end of these lines. Infinite lines are used to represent lines with a particular slope, such as horizontal or vertical lines.
You can change an infinite line to a finite line using Clip or a finite line to an infinite line using Infinite.