Parallel venation refers to a pattern in the veins of a leaf where the secondary veins run parallel to each other off of a central, perpendicular primary vein. Parallel venation is also sometimes used to describe a similar pattern on an insect's wing.
Venation is a general term for the pattern of veins on a leaf. Venation patterns help with plant identification. The parallel variation features a large primary vein, called a mid rib, running the length of the leaf and smaller secondary veins branching off in a nearly perpendicular fashion running parallel to each other. Much smaller, fine veins run between the parallel veins forming a web of veins to nourish the leaf.