The gold coloured 'count' wheel arm (correctly called a driving pawl or gun lever) pushes the 'count' wheel around by one tooth every 2 seconds, as it travels from left to right. One of the teeth in the 'count' wheel is cut deeper than all the others, and the effect is for the little pin (circled blue), that engages with the teeth, to go deeper when it encounters this tooth. This causes the right hand end (circled red) of the 'count' wheel arm, which is balanced slightly heavier on the left hand side, to tip upwards. On normal operation this arm will pass through the rectangular hole that you can see in the vertical latching arm (or stirrup).
However when the end tips upwards it is no longer able to pass through the hole and instead pushes the latching arm out of the way.
This causes the weighted impulse arm, that the latching arm was originally holding up, to now fall downwards. There is a little roller on this arm which subsequently falls onto a pallet connected to the pendulum rod to give it an impulse. The picture seen here explains this.