From the docs:

"Prerequisites

To issue an EXPLAIN PLAN statement, you must have the privileges necessary to insert rows into an existing output table that you specify to hold the execution plan.

You must also have the privileges necessary to execute the SQL statement for which you are determining the execution plan. If the SQL statement accesses a view, then you must have privileges to access any tables and views on which the view is based. If the view is based on another view that is based on a table, then you must have privileges to access both the other view and its underlying table."

So make sure there is a PLAN_TABLE they can insert into, and make sure they have SELECT on the tables the queries will be on.

Hope this helps.