The swing plane is an often discussed and important component of swing mechanics. In most cases when we speak of the swing plane, we are addressing the trajectory of the bat as viewed from across the plate. From the across the plate view, we can see the trajectory of the bat-head in the contact zone - was it angling downward, level or on an up-slope in the contact zone.
Across the plate view of the swing plane
I have found that understanding the nature of the "swing plane" as viewed from the mound is also a key component to understanding good swing mechanics. Think of the plane of the swing from this view as looking at the edge of a flat disc that is tilted down toward the plate so as to intersect the path of the ball in the contact zone. From the frontal view, the bat, lead-arm and elbow should all be in that plane (flat disc) from the initiation of shoulder rotation to contact.
The batter may have the bat more vertical than the plane while in his stance, but the bat must be sweep cleanly behind the head and into the plane of the lead-arm when shoulder rotation begins. When the bat is accelerated down through the plane of the lead-arm, the trajectory of the bat will appear more like a sine wave than a flat disc. This will lead to inconsistent contact and often results in weak grounders or pop-ups.
Below are frontal views of Sammy Sosa-s (2003) and Bobby Abreu's (2005) swing planes when they won the Home Run Derby.
Frontal view � Sosa swing plane
Frontal view -- Abreu swing plane
Here is A-Rod's swing plane in the 2003 Home Run Derby.
Frontal view � A-Rod 2003 swing plane