The definition of a puch shot might be a bit subjective (it depends on who you ask). But generally it is a shot with an abbreviated swing, especially an abbreviated follow through. Depending on who is playing the shot and the situation they may call it a punch shot, a knockdown shot, a squeeze or other names.
Why would you want to hit a punch shot?
You see the pros on TV hit punch shots all the time. There might be many reasons for hitting a punch shot, but the most common reasons are:
-    To keep the trajectory of the shot down lower than usual (useful in the wind)
-    To have better feel for the force applied to the shot, distance control (useful when the specific yardage you need is between clubs)
-    To decrease the amount of spin on the ball (assuming decent contact, the harder the ball is hit the more spin the ball will have on it – and good players don’t always want the maximum amount of spin on the ball)
-    The backswing or follow through are obstructed in some way (unavoidable at times when you find yourself in tree trouble)
Here’s a situation that comes to mind where I would play a punch shot. You have left yourself 80 yards for your approach shot to a par 5, with the wind blowing against you quite strongly. You have no bunkers or water to go over with the shot and the pin is located towards the back of the green. If you hit the shot using your usual set up and full swing using a pitching wedge, the ball will get a lot of height and consequently be affected by the wind a lot more than a lower shot would be. Because we have a lot of grass between ourselves and the hole and no hazards to go over, it makes more sense to hit a low punch wedge in to the green, allowing us to pitch the ball short of the hole and let it bounce up towards the hole, checking on the second or third bounce.
How to hit a low punch wedge
The key to hitting this shot correctly is the way we position our body before we swing – the set up position
Set-up position
-    Position the leading edge of your club at a 90 degree angle to the ball to target line
-    Make your usual grip
-    When making your stance, the feet should be placed approx the same width as your shoulders, with the left foot poiting a little toward the target to allow for an easier turn of the hips
-    The ball should be positioned well back in the stance just opposite the inside of the right foot.
-    The hands are in their normal position, opposite the inside of the left thigh. This automatically sets your hands much further ahead of the ball than normal, which delofts the club and creates the steep, downward blow necessary to play a successful shot of this type
-    Your body weight will be approx 65% on the left foot, 35% on the right foot
The swing
The length of the swing will depend on how far you need the ball to travel. Keep your backswing compact and maintain the relationship created between the hands and the clubface at set-up through impact. The feel of the shot will be an aggressive strike – punching the ball forward and low towards the target. The follow through will take most of your weigth onto your lefr foot, with the arm swing shortened a little due to the downward impact on the ball.