The overhead shot is the most important shot in badminton.
It allows you to hit the shuttle at the highest point, by doing that you
a. will be able to take away reaction time from your opponent
b. allows greater deception
c. allows maximum power stroke, by making full use of arm extension (Lever)
Basically, all coaches will teach this shot as it is the most fundamental stroke. One can hit a drop, clear and a smash from this shot.
The overhead can be liken to a throwing action. Basically you stand on a sideway position and then 'open' up with your racquet arm. Your non-racquet arm points to the direction of the incoming shuttle, this is important for balance and follow through.
Next the sequence is the hitting action. Which can be a drop; which you lightly tap the shuttle slightly in front to force the shuttle to travel near the net.
The clear is you hit the shuttle slightly behind you so that it travels high and far.
The smash is hit with pace and with the wrist in a downward action.
This cartoon illustrates the hitting action of the overhead stroke.