Going back to the basics, the sear is the part that keeps the tumbler from turning. It does this by moving into the full cock or half cock notch.
Pulling the trigger causes the blade on the top of the trigger to push on an arm which is a part of the sear.
In the picture above, you can see the sear nose engaging the full cock notch on the tumbler.
If the sear moves downward it loses its grip on the full cock notch and the tumbler will begin to rotate counterclockwise in this picture.
With a simple trigger, the fairly heavy pressure that is being applied to the trigger by the shooters finger will tend to cause the sear to continue to move downward and away from the tumbler so, by the time the half cock notch (just to the left of the full cock notch) gets to where the end of the sear used to be the sear will be well clear of the half cock notch allowing it to go whizzing by while the hammer falls to the fired position.
Now, if it only took a very light amount of finger pressure on the trigger to release the sear from the full cock notch, the sear wouldn't move away from the rotating tumbler and there is every possibility that it will try to enter the half cock notch. If it does enter the half cock notch, everything will come to a screeching halt and the least that will happen is, the hammer will stop falling. The worst that can happen is the nose of the sear or the half cock notch or, both will be broken.
Now, enters the "fly" into the picture. (Well, not really. The lock shown doesn't have a fly in it.)
The fly is a very small part that can rotate back and forth. It is located right at the half cock notch and is inserted into the tumbler. If it is shoved toward the full cock notch by the nose of the sear while the gun is being cocked, it will expose the half cock notch so, if the shooter decides to lower the hammer while the sear is lined up with the half cock notch, the sear will enter it and the gun will be at "half cock" or in the "safe" condition.
If the shooter does not stop pulling the hammer back, the nose of the sear will ride up over the fly and end up entering the full cock notch making the gun ready to fire.
When the trigger is pulled, even with a light pressure, as long as the pressure is enough to cause the sear to disengage from the full cock notch, the tumbler will begin to rotate counterclockwise while the hammer is falling.
When the nose of the sear gets to the fly, it pushes it forward causing it to cover up the half cock notch. With the half cock notch covered, the nose of the sear can't enter it so instead, the sear pushes harder on the fly which causes the sear to raise up slightly and jump over the fly. That allows the hammer to continue to fall and fire the gun.
As Rudyard says, the fly was originally made to be used with "set triggers". The "2 trigger" guns that are on a lot of muzzleloaders.
Set triggers release the sear from the tumbler by striking the sear arm with a spring loaded blade. This causes a momentary movement of the sear causing it to disengage from the full cock notch but without the heavy finger pressure pulling the trigger, the sear almost instantly moves back against the outside of the tumbler. With a fly in the tumbler, the fly blocks off the half cock notch to prevent the sear from engaging the half cock notch.
Clear as mud? Hopefully it answers the question.