SYSDBA and SYSOPER are roles in Oracle. The SYSDBA privilege is assigned to a user account and gives that account the same privileges that the INTERNAL account has. This role includes all system privileges including ADMIN OPTION, which allows granting system privileges to other users. When you log in as SYS user you have to log in as SYSDBA. In summary it allows any database administration activity to take place by the user with SYSDBA privileges.
The SYSOPER privilege is assigned to a user which will perform operator type activities. Any user with SYSOPER role can do startup,shutdown,alter database open/mount and backup of database, archiving and recover etc.
Hope this helps