What is an artificial (derived) primary key? When should it be used?

Using a name as the primary key violates the principle of stability. The social security number might be a valid choice, but a foreign employee might not have a social security number. This is a case where a derived, rather than a natural, primary key is appropriate. A derived key is an artificial key that you create. A natural key is one that is already part of the database.

whether artificial primary key is equvalent to the row_id of the table or it is the the combination of the previous primary key field and the new field which creates the importance of it.

Many at times Natural Keys are based on Categorizations that are perceived permanent.However due to natural or artificial changes these nomenclatures bacome meaningless for the new transactions.It is also true that with the new transactions Natural Keys might loose their importance.Such are the situations with Slowly and Fast changing dimensions.

To avoid this Surrogate Keys are used that are Auto Generated, are Integer Keys and they take less query execution time.

It is a system-assigned number that is unique for each row of data in a table.  It is used by database administrators to allocate rows of evenly and efficiently on data storage / servers. 

A derived key comes from a sequence. Usually it is used when a concatenated key becomes too cumbersome to use as a foreign key.