What is the purpose of Order By 1 in SQL select statement?

This is useful when you use set based operators e.g. union

select cola
  from tablea
union
select colb
  from tableb
order by 1;

This:

ORDER BY 1

...is known as an "Ordinal" - the number stands for the column based on the number of columns defined in the SELECT clause. In the query you provided, it means:

ORDER BY A.PAYMENT_DATE

It's not a recommended practice, because:

1. It's not obvious/explicit
2. If the column order changes, the query is still valid so you risk ordering by something you didn't intend