From the 11g Oracle Documentation:
SYS AND SYSTEM Users
The following administrative user accounts are automatically created when you install Oracle Database. They are both created with the password that you supplied upon installation, and they are both automatically granted the DBA role.
This account can perform all administrative functions. All base (underlying) tables and views for the database data dictionary are stored in the SYS schema. These base tables and views are critical for the operation of Oracle Database. To maintain the integrity of the data dictionary, tables in the SYS schema are manipulated only by the database. They should never be modified by any user or database administrator. You must not create any tables in the SYS schema.
The SYS user is granted the SYSDBA privilege, which enables a user to perform high-level administrative tasks such as backup and recovery.
This account can perform all administrative functions except the following:
Backup and recovery
While this account can be used to perform day-to-day administrative tasks, Oracle strongly recommends creating named users account for administering the Oracle database to enable monitoring of database activity.
SYSDBA and SYSOPER System Privileges
SYSDBA and SYSOPER are administrative privileges required to perform high-level administrative operations such as creating, starting up, shutting down, backing up, or recovering the database. The SYSDBA system privilege is for fully empowered database administrators and the SYSOPER system privilege allows a user to perform basic operational tasks, but without the ability to look at user data.
The SYSDBA and SYSOPER system privileges allow access to a database instance even when the database is not open. Control of these privileges is therefore completely outside of the database itself. This control enables an administrator who is granted one of these privileges to connect to the database instance to start the database.
You can also think of the SYSDBA and SYSOPER privileges as types of connections that enable you to perform certain database operations for which privileges cannot be granted in any other way. For example, if you have the SYSDBA privilege, then you can connect to the database using AS SYSDBA.
The SYS user is automatically granted the SYSDBA privilege upon installation. When you log in as user SYS, you must connect to the database as SYSDBA or SYSOPER. Connecting as a SYSDBA user invokes the SYSDBA privilege; connecting as SYSOPER invokes the SYSOPER privilege. Oracle Enterprise Manager Database Control does not permit you to log in as user SYS without connecting as SYSDBA or SYSOPER.
When you connect with the SYSDBA or SYSOPER privilege, you connect with a default schema, not with the schema that is generally associated with your user name. For SYSDBA this schema is SYS; for SYSOPER the schema is PUBLIC.