On the BECOME USER privilege, Oracle docs offer this information:

BECOME USER Report

The BECOME USER Report shows all database accounts roles that have the BECOME USER system privilege. This is a very powerful system privilege: it enables the IMPORT_FULL_DATABASE and EXPORT_FULL_DATABASE roles for use with Oracle Data Pump. Accounts that possess this privilege can be misused to get sensitive information or to compromise an application.

On Oracle DBA Forums, users have shown interest in the often mysterious BECOME USER privilege.  The  "BECOME USER" privilege does, in fact, exists. Try this query:

SELECT * FROM DBA_SYS_PRIVS where privilege = 'BECOME USER';

-- Here we see that the imp_full_database has the become user privilege.

 Jeff Hunter also has an article in which he informs us that:

The "BECOME USER" System Privilege is one that has stirred up a lot of confusion amoung DBAs and developers. Oracle unfortunately does not support or comment on the use of this system privilege. I believe that import uses it to import objects in the schemas of other users.

Oracle has an undocumented OCI function called upicuithat will allow a given oracle user to become another user. This user has to have the "BECOME USER" system privilege.  

Some users find this similar command useful, although BECOME USER has specific usefulness in the import (impdp) utility of Data Pump;

"You have probably seen in SQLPLUS where you can issue the command

connect user/password