Welcome to the forum.
The fly is located at the mouth of the half cock notch in the tumbler. The flys job is to rotate out of the way and expose the half cock notch when the hammer is being raised from the fired position, allowing the nose of the sear to enter the notch.
When the hammer is raised further the nose of the sear jumps over the fly and continues until it (the sear) falls into the full cock notch.
When the sear is released from the full cock notch, IF the trigger was a "set" "set trigger" the sear is only momentarily moved out of the full cock notch. Then the sear spring will push the nose of the sear back against the outside of the tumbler.
As the hammer falls, the nose of the sear will come back to the fly and push it forward. In this forward position the fly will block off the entrance to the half cock notch forcing the sear to "jump over" it. This allows the hammer to continue to fall to the fired position.
In guns that do not have a "set trigger" or a fly in the lock the shooters finger will hold the trigger to the rear which in turn keeps the sear raised up off of the outside of the tumbler.
In this raised position the half cock notch will pass by the sear without a problem as the hammer continues to fall.
While I'm writing, although you did not ask about set triggers you might be interested in the following:
There is one type of set trigger that is made for use with locks that do not have a fly.
This type of set trigger is known as the Double Set Single Lever trigger.
It is designed so that if it is not set or has been released from a set condition its lever always pushes up on the sear arm causing the nose of the sear to clear the body of the tumbler.
With this type of trigger the shooter must first set the trigger before cocking the gun. If he tries cocking the gun without first setting the trigger it will not engage the full cock notch.
Because the lock cannot be set unless the rear trigger is "set" the front trigger does not have to be able to fire the gun when the set trigger is not set.
As the front trigger doesn't need to be able to fire the gun by itself, set triggers of this style do not have a lever or blade on the front trigger. This explains why they are called Single Lever triggers.
These triggers are usually found on target rifles.