That answer depends upon what class of cabin you have booked. Per NCL's new Freestyle 2.0 program of perks:
Inside and Oceanview, you can reserve a table that night.
Balcony and Mini-Suite, you can reserve a table tomorrow night and tonight.
Suite, you can reserve a table every night.
That's for Specialty Restaurants.
The Main Restaurants and the Buffet don't require reservations, never have.
Of course, if you're wishing to reserve a table, or several tables for a large group, you can reserve them at the Main Restaurants too, just to make sure you can all sit down together.
Usually groups can only reserve tables early or late, not during the ever most popular 7 pm time slot.