The term persistent object comes from 'persistence' which indeed means the 'permanent storage'.
Persistent Objects are the ones who give an indication that the state of an object would be permanently stored even after the execution of the program.
Permanent Storage -- is nothing but the place from which we can retrieve at a later point of time. Say a filesystem (file in your folder) or the database table.
Storing it as a part of your application collection say HashMap, ArrayList may NOT be a persistent as the values in the objects (and the objects themselves) would be lost after the execution of the program.