TWO_TASK is an environment variable. If you set TWO_TASK=foo, then "sqlplus scott/tiger" is equivalent to "sqlplus scott/tiger@foo". If TWO_TASK isn't set, then "sqlplus scott/tiger" will connect to the local database, and throw an error if there isn't one. That's all there is to it; it means you can do a TNS connection while thinking you're doing a local connection. You can think of it as a "default database alias" if you like, but probably best to think of it as what it is.
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