It's not necessarily as simple as that.
It is going to depend on a number of factors:
1) Do you have the source code to both applications?
2) If not, does the other application expose an API to access data from it?
3) If not, can you do magic?
If you have the source code, and you will always ask Application A for info, then I would look at the
Socket[
^] or
TCPListener[
^] classes.
If the Application exposes an API, then you need to look at the application - they are all different, so I can't be specific.
If neither of these, then the API you need is called
PnP[
^]