Agile teams use physical boards to run Scrum or Kanban.
Cards can be printed out using JIRA 7+ "Print cards" functionality or any 3rd party print plugins as Agile Cards from SPARTEZ
Using the Agile Tools & Filters the board can be filtered first and only visible tasks will be printed out.
Additionally the Scrum Master can pre-define sets of private filters for printing only.
Print unprinted issues
Lesson 6 - Printing selected cards from the board & backlog tutorial