How to know or recover my pg_dump password? I would like to backup my Postgre db using pg_dump. However, the first question asked by the prompt is the password. 
But I have no idea what it is. Indeed, it is different from my admin account password, and I don't know where to find it or recover it.
pg_dump does not have a password specific to itself.  You run pg_dump as a certain database user (often the user spelled 'postgres', but not always), and authenticate however that user would authenticate for any other (non-pg_dump) connection.  So your question really has nothing to do with pg_dump.

You probably can't recovery the password (unless you are willing to crack md5 hashes to brute force it--which is really only feasible with poor passwords or with big bucks), but you can use your "admin account" to reset the password to something you do know.  How you do that depends on whether "admin account" means a database superuser account, or an OS account for the OS user who owns and runs the database files.  Also, it might depend on your settings in pg_hba.conf.