How ATP is formed during the photophosphorylation

You have followed the path of the electron through the electron transfer system and although it was indicated at what point ATP is formed, it was not explained how this takes place. An explanation follows. You need to understand photophosphorylation and chloroplast anatomy to understand this process.

The molecules of the electron transfer system occur in the thylakoid membrane alongside the photosystems. As an electron is passed along the electron transfer systems, a hydrogen ion is transferred across the thylakoid membrane from the outside of the membrane (the stroma of the chloroplast) into the thylakoid compartment. This takes place as plastoquinone transfers the electron to the cytochrome complex. The splitting of water in the first step of the chain also leads to the release of hydrogen ions into the thylakoid compartment. 

As more and more electrons are passed along the electron transfer system, the number of hydrogen ions in the thylakoid compartment increases i.e. their concentration increases. Eventually there is a higher concentration of hydrogen ions inside the compartment than outside in the stroma. There now exists a potential energy gradient across the thylakoid membrane as the hydrogen ions want to move from an area of higher concentration inside the compartment to an area of  lower concentration in the stroma. They are prevented from doing so unless they move through a special enzyme molecule called ATP synthase. As the hydrogen ions move through ATP synthase their energy is captured to make a high energy bond between an ADP molecule and a phosphate molecule forming ATP. The ATP formed this way is now transferred to the light independent phase of photosynthesis (Calvin cycle).