Because the missions of the many NIH institutes and centers that award grants have some overlap, secondary assignments (also called dual assignments) of applications give program officials a comprehensive view of all potentially interesting projects. They can follow a secondarily assigned project through review and subsequent years of support as a way to stay informed.
Rarely, if a project scores well and is not chosen for funding by the primarily assigned institute or center, a program official from the secondary institute or center may seek to fund the application. This may sound promising if your application is in the payline gray zone for your primary institute or center, but these pickups occur for less than 2% of dually assigned applications that are not involved in a special funding initiative.
So, what should you, the investigator, do when you see a secondary assignment has been made? No action is required. Some investigators contact the program official who is monitoring the application as a secondary assignment to remind him or her to look again at the application and consider it for funding. If you want to request primary and secondary assignments, you can do so in your cover letter. There are instructions on how to do so in the application guide.