Swing plane describes the path and the angle of the club shaft as it moves around your body when you swing.
If you have a two plane golf swing, you will tend to set up more upright than a golfer using a one plane method. Your arms will hang more vertically from the shoulders and you will stand closer to the ball than a golfer using a one plane method. A two plane takeaway sees the shaft of the club parallel to the target and in line with the toes.
However, the most distinctive movement with a two plane swing is that the arms move more independently of the rotation of the body. During a two plane backswing, the arms move more steeply or on a more upright plane than the shoulders do, as the shoulders rotate on a flatter plane. The left arm will disconnect from the chest movement to create more width and the body will shift slightly to the right. At the top of the backswing, the arms will drop down on to the flatter plane before the body can aggressively rotate into the downswing. The hips will rotate and shift to the left and the left arm and the club shaft are on plane just before impact, with the right arm pointing outside of the target line. Through impact, the arms and club will mirror the backswing and stay in front of the body with the right arm rotating over the left as the body turns through impact and this continues into the follow through.
Try this drill to determine whether you are suited more to a one plane or two plane golf swing. First, stand further away from the ball, bend over and hold your driver like a hockey stick. Swing the club around you on a flat plane and hit some golf balls. Once you have done this, stand more upright and hold your driver with your usual grip. Swing back and then push your hips towards the ball before you swing your arms through.
If you hit better shots with the hockey style swing, you are probably a one planer. If you hit better shots from the more upright position, you are likely to be a two planer.