Android OS and postgreSQL
I would write a RestFUL API or WebService to be used as front end for your Android device to connect to your PostgreSQL backend.
I don't think you will be able to connect directly your Android App to a PostgreSQL database.
I'd go with a lightweight REST interface that would talk to PostgreSQL in the backend. Have a look at Simple.
I would approach this by implementing an intermediary web service. The Android application would send requests to the web service, which would serve as a gatekeeper to isolate the PostgreSQL server from the internet at large.