What is happening in the park later that evening and who is involved?

In Part One, Chapter Two, the reader learns that an execution is due to take place that evening in the park:

Some Eurasian prisoners, guilty of war crimes, were to be hanged...This happened about once a month and was a popular spectacle.

These public executions are, thus, a constant presence in the lives of the citizens of Oceania. Even children are encouraged to attend and this explains the excitement and over-zealous behaviour from the Parsons...

In Part One, Chapter Two, the reader learns that an execution is due to take place that evening in the park:

Some Eurasian prisoners, guilty of war crimes, were to be hanged...This happened about once a month and was a popular spectacle.

These public executions are, thus, a constant presence in the lives of the citizens of Oceania. Even children are encouraged to attend and this explains the excitement and over-zealous behaviour from the Parsons children when Winston visits their flat to carry out some repairs. 

That the party practices such violence in public is representative of the extent of its control. Executions are visual reminders of the consequences of rebellion and thus act as a strong deterrent to people like Winston. It is interesting to note that the park is the setting for a chance encounter between Winston and Julia in Part Three, Chapter Six, after their imprisonment in the Ministry of Love and 'reintegration' in society. The park is therefore a symbol of the party's power and its unfaltering ability to weed out rebellion and transform it into love for Big Brother.