The Abstract Syntax is the information which constitutes the common knowledge that communicating applications must share.
It can be seen as some abstraction of the Transfer Syntax, as it consists in removing from the definition of the Transfer Syntax all the elements related to the representation of the values, to focus on the interpretation of the form of these values.
Two applications can communicate only if they share the same definition of Abstract Syntax for the Application Data Values they want to be able to exchange.
Note that the Abstract Syntax does not include at all the other data (i.e. the ones which are not involved in the exchange, but are private to a given application).
The definition of the Abstract Syntax is an integral part of the specification of the application.