TWO_TASK mocks your TNS ALIAS which you are going to use to connect to database. Let’s assume you have database CLIENT with TNS alias defined as PROD to connect to Database PROD on machine teachmeoracle.com listening on port 1521. Then usual way to connect is sqlplus username/passwd@PROD; now if you don't want to use @PROD then you set TWO_TASK=PROD and then can SIMPLY use sqlplus username/passwd then sql will CHECK that it has to connect to TNS alias define by value PROD i.e. TWO_TASK

TWO_TASK mocks your TNS alias which you are going to use to connect to database. Let’s assume you have database client with TNS alias defined as PROD to connect to Database PROD on machine teachmeoracle.com listening on port 1521. Then usual way to connect is sqlplus username/passwd@PROD; now if you don't want to use @PROD then you set TWO_TASK=PROD and then can simply use sqlplus username/passwd then sql will check that it has to connect to TNS alias define by value PROD i.e. TWO_TASK